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i  . 

14  5  6 


HARMONY 


ON   TB8 


Inductive  Method. 


BY  HUGH  A»  CLARKE, 

Professor  of  Music,  University  of  Pennsylvania. 

•--■;'  ■'%' 

PHUiADSU'HIA : 

L  E  I-:     c*(;    W  A  T .  Iv  E  R, 

No.  1113  Chestnut  Street. 


Coprrighl,  1880.  bj  Lu  *  WilKlm. 


It 


: 


^•r.^'ffv--- jc^--- 


(A 


^^ 


«A 


^ 


t 


INTRODUCTION. 

This  book  makes  no  claim  to  be  a  new  theory  of 
Imrmviny;  but  merely  a  new  eystcm  of  teaeliiii-j; 
harmony,  by  what  in  universally  recognized  as  the 
best  method  of  teaching,  viz.,  the  inductive. 

The  theory  of  harmony  is  the  province  of  the 
acoustician,  not  of  the  musician.  It  is  often  asserted 
that  music  has  gained  largely  by  the  labors  of  the 
acousticians;  but  this  is  not  so  evident,  when  we 
remember  that  all  the  best  music  was  written  before 
the  science  of  acoustics  was  born.  The  instinct  of 
genius  discovered,  afcer  many  trials  and  mistakes, 
what  combinations  and  successions  of  sound  were 
agreeable  and  expressive,  without  asking  or  caring 
why.  And  the  science  of  sound  has  made  but  little 
advance  in  explaining  this  "why;"  and  has  not 
added  one  chord  or  progression  that  was  not  known 

to  Bach. 

Science  can  analyze  sounds,  but  not  music.  It 
can  say  to  what  the  various  qualities  of  sound  are 
to  be  attributed;  but  can  give  no  explanation  of 
their  effect  on  the  emotions.  Indeed,  the  best 
authorities  on  acoustics,  viz.,  Ilelmholtz,  Pole,  Parry, 
are  agreed  that  it  is  useless  for  tlie  musician  to 
theorize  as  to  the  origin  of  chords.  It  is  enough 
for  him  to  know  what  combinations  and  progressions 


if 


iMHIKi'-' 


r-^ 


4  INTIlOlit  CTION. 

praclit't'  iiiul  t'X]K  .it'iiCf  li:ivi'  proved  fr'xxl.  >'o 
lictlcr  proof  is  icciuirctl  of  tlin  nscU'ssiicss  of  this 
tlicorizing  iibout  Iho  orifriii  of  cliords,  tluiu  tlic 
divprsily  of  views  witli  n'giird  to  tlio  origin  of  the 
minor  clionl  ;  o\ving,to  the  fiiot,th!it  its  thinl  rannot 
bo  an  ovi'rt(«io  of  its  fiindamental. 

Tho  object  of  the  writer  on  harmony  and  compo- 
Hition  ought  to  be,  to  reduce,  to  some  Hystem,  the 
mass  of  facts  (for  want  of  a  better  name)  of  v.liioii 
our  modern  miisie  is  tlie  outgrowtii.  These  facts 
are: 

Ist.  A  te?npered  scale. 

2(1  (and  resulting  from  tlie  llrst).  A  number  of 
keys  related  in  many  ways. 

3d.  The  possilile  combinations  of  sounds,  called 
chords. 

4th.  The  seeming  rules  tliat  govern  the  successions 
of  these  combined  sounds.  Rules,  be  it  remembered, 
that  are  not  the  i-xpression  of  some  natural  fact ; 
but  are  merely  the  residt  of  a  consensus  of  tlie  best 
taste  in  the  art. 

Tliese  foui'  facts  make  up  tlie  substance  of  har- 
mon;/,  and  form  tho  groundwork  of  composition, 
which  deals  chiefly  with  melody  and  form. 

Many  departures  will  be  found  in  this  work  from 
the  usual  methods  of  teaciiing,  notably  the  following  : 


.. 


1st.  With  regard  to  the  formation  of  the  minor 
scale. 


}.'00(|.        >'o 

■iiH'ss  of  tliiw 
lIs,  tlinii  tilt' 
origin  of  tlio 
( tliir<l  raniiot 

:  mikI  fonipo- 

i"    H\'Kt0in,  tllf 

me)  of  v.iiicii 
Th.'sc  facts 


A  iminl)or  of 

ounds,  called 

10  successions 

renicmbcred, 

natural  fact ; 

IS  of  the  best 


tance  of  har- 
eomposition, 
rm. 

lis  work  from 
the  followin;^ : 

of  the  minor 


II 


INTHODI  I'TloV.  n 

2d.  Till'  11  ferrinn  of  nil  (lis:<()iiiint  chords  to  two 

roots. 

3d.  The  disoardiiij,'  of   Mh'  time-honored    ligured 

bass. 

4tli.  The  formuhitinjj  of  simple  rules  for  modula- 
tion. 

My  reason  for  the  ilrst  departure  is,  that  the  rela- 
tionship and  signature  of  the  minor  scale  is  thereby 
n.xed  at  once  in  the  nienuuy  of  the  pupil. 

For  the  second.— That  it  reduces  the  confiisiii-r 
multiplicity  of  rules  for  the  use  of  elioids  with  the 
seventh,  to  four  that  have  no  exceptions. 

l"'or  the  third.— That  it  is  a  hindrance,  rather  than 
a  helj),  to  the  pupil.     The  author  has  had  numbers 
of  i)upil3  who  could  write  or  play  a  fij,nired  bass ; 
but  Avho  were  quite  in  the  dark  as  to  the  reasons 
why  they  used  such  successions  of  chords.     Many 
of  these  pupils  Irul  spent  one  or  two  years  studying 
with  good  masters.     And  have  themselves  acknowl- 
edged that  they  have  learned  more  in  a  month,  on 
the    itlan    pursued    in  this  work,  than   in  all    their 
previous  studies.     It  has  always  been  to  the  author 
a  mystery,  why  figured  basses  were  used  for  teaching 
harmony.     They  were,  originally,  a  sort  of  musical 
shorthand;  and,  in  these  days  of  cheap  music,  are 
only  a,  survival  of— not  by  any  means— tlu;  fittest. 
The  iiiithor  is  often  met  with  the  argument  that  ''all 
the  great  nuif.ieiau.  learned  thi.^  way."'     Well,  the 


Ml 


INTKOKIlTlON. 


pity  is,  they  had  not  a  better  and  ciisicr  way.  It  it* 
no  nrgunu'nt,  that  liocausc  a  man  is  a  great  poet, 
therefore  the  system  pursued  in  teaching  him  hiH 
IctterH  waH  the  best  i)OHBible. 

With  regard  to  tin-  fourth  de).arture  from  usual 
prnetice.—Tlie  author  feels  a  pardonable  pride  in 
having  reduced  the  art  of  modulation  to  four  simple, 
easily'  understood  and  comprehensive  rules.  Hitherto 
the  plan  followed  in  teaching  modulation,  has  heen 
to  give  th>>  pu|)il  various  examples,  wliich  were  to 
be  transposed  to  all  (he  keys,  until  they  were  II xed 
— parrot  fashion — in  his  memory.  When  ho  wisiied 
to  make  a  modulation,  he  m\ist  remember  one  of  his 
"  patterns."  Hy  mastering  the  rules  her«  given,  the 
pupil  can  make  his  own  modulations  in  endless 
variet}-,  iind  make  them  understandingly. 

It  is  well  to  bear  in  mind  that  music  is  an  art, 
not  a  science ;  although  the  8tud.v  of  harmony  is 
often  wrongly  called  the  science  of  music.  The 
rules  of  musical  construction  are  not  the  result  of 
scientilic  investigation;  l)ut  are  deductions  from 
the  practice  of  those  distinguished  by  their  artistic 
eminence.  Many  musicians  think  these  rules  are 
the  expressions  of  some  natural  law.  Many,  not 
musicians,  think  they  are  tlie  arbitrary  and  often 
unreasonable  dicta  of  musicians.  IJnt  botii  are 
wrong.  Good  taste  is  the  only  arbiter  in  matters  of 
art.  And  since  the  standards  of  tnste  vary  with 
every  period  of  the  world's  history,  it  is  not  possible 


p  way.     It  is 

great  poet, 

ling  liitn  his 

!  from  usual 
ble  |iri^lt!  in 
four  Himplu, 
OS.  Hitherto 
on,  lias  i)cen 
liieii  were  to 
ly  wore  fixed 
3n  he  wished 
er  one  of  his 
r«  given,  the 
i   in   endlcHS 

nc  i8  nn  art, 

harmony  is 

music.     The 

till'  result  of 

ictions   from 

their  artistic 

se  rules  are 

Many,  not 

y  and   often 

ut    ixitii   are 

in  matters  of 

to  vary  witli 

not  possible 


} 


INTBOIU'CTION.  T 

to  give  to  any  of  itH  decisions  the  nt^imp  of  perma- 
nency, and  say :  ThlH  is  ft  rule  that  can  never  be 
broken. 

In  conclusion,  the  author  would  express  h.s  tlmnks 
to  his  numerous  pupils,  both  present  and  p.st,  for 
the  warm  interest  they  huve  iMken  in  the  progress 
of  this  work,  and  for  their  kind  wislu's  and  iu<iuirie» 
from  all  parts  of  the  country. 

IT.    A.    CT.AIIKK, 

Profriior  of  Mutic  al  the  VnivertUy  of  Pe  .  tylvania. 


Philadelphia,  Novemher  15, 1880. 


I 


W 


PRELIMINARY  DEFINITIONS. 


1  _A  degree  means  from  one  letter  to  the  next,  whether  a 
whole  or  half  tone. 

2.— Chords  and  intervals  are  always  counted  up  from  tho 
lowest  Ltter.  In  counting  the  number  of  letters  in  an  inter- 
val, both  letters  are  included,  thus :  C— D,  is  a  second,  two 
letters  being  included ;  C— F,  is  a  fourth,  four  letters  being 
included,  and  so  on. 

3.— A  chromatic  change  retains  the  letter,  but  alters  the 
pitch,  thus :  C— C#,  is  chromatic.  A  diatonic  change  changes 
both  the  letter  m1  the  pitch,  thus  :  C— D,  or  E-F,  are  diatonic, 
although  on  's  a  whole  tone,  the  other  a  half  tone.  An  enhar- 
monic change  retains  the  pitch,  but  changes  the  letter,  thus: 
C#— Dl»,  F— E#,  G— FX,  «tc. 

4. The  word  base  is  used  to  indicate  the  lowest  note  of  a 

chord,  without  regard  to  its  pitch.     The  word  bass  (trota  the 
Italian  ba»io\  uieans  a  low  or  deep  sound. 

5.— A  diatonic  scale  is  one  that  includes  all  the  seven  letters, 
without  omission  or  repetition.  (There  are  various  kinds  of 
diatonic  scales,  viz. :  The  Greek,  the  Gregorian  and  the  modern. 
They  differ  in  the  arrangement  of  the  tones  and  semitones. 
The  modern  resemble  two  of  the  ancient  scales,  in  their  arrange- 
ment of  tones  and  semitones ;  but  differ,  in  being  tempered 
(i.  e.,  a  little  out  of  tune).  For  explanation  of  tempered  scales 
see  Helmholtz,  or  Stainer's,  or  Groves'  Dictionary). 


I 


(8) 


\ 


ONS. 


?  next,  whether  a 


iteJ  up  from  tho 
Iters  in  an  inter- 
is  a  second,  two 
our  letters  being 


r,  but  alters  the 
10  change  changes 
1— F,  are  diatonic, 
tone.  An  enhar- 
the  letter,  thus : 


I  lowest  note  of  a 
rJ  bats  (tram,  the 


the  seven  letters, 
3  various  kinds  of 
a  and  the  modern. 
33  and  semitones. 
!,  in  their  arrange- 
1  being  tempered 
)f  tempered  scales 
)nary). 


> 


CHAPTER  I. 

1.  An  Inters-al  is  the  difTerenee  in  pitch  between 
two  sounds. 

2.  The  name  of  an  interval  depends  upon  the 
number  of  letters  it  includes ;  the  kind  of  interval 
upon  the  number  of  semitones  it  includes. 

3.  There  are  five  HHr7s  of  intervals,  viz.:  Major, 
minor,  augmented,  diminislied  and  perfect. 

The  following  table  contains  all  the  kinds  of  seconds,  thirds 
and  fourths. 

Thirdt.  Fourlhi. 


Seconds. 


^^^^^^^E^l^-I^^^ 


Semitones  \  2 

MIn.     Moj. 


3 
Aujt. 


a         3         4        5  4         6        6 

Dim.  MIn.  Mnj.  Aug.  Dim.  Per.  Aug. 


4.   By  inverting  these   intervals  we   get  all  the 
kinds  of  sevenths,  sixtlis  and  fiftlis. 


Sevenlhi. 

-^ — -o — o- 


Sixths. 

-fil — s- 


:=g^liE|B^^^^^^^ 


Fifth: 
-O — r« — r»- 


Semil<>B<-i  11       10         U 

MaJ.  MIn.  Dim. 


10       9        8        7 
Aug.  Maj.  MIn.  Dim. 


8         7       0 
Aug.  Per.  Dim. 


f.  On  examination  it  will  be  found  that  the  inver- 
sion of  a  second  produces  a  seventh;  of  a  third,  a 
sixth;  of  a  fourth,  a  fifth.  Also,  tiiat  an  interval 
and  its  inversion  together  make  an  octave— and,  as 

(9) 


n 


! 


ii.^^ 


10 


ci.abke's  harmony. 


the  octave  contains  twelve  semitones,  an  inttTval 
and  its  inversion  must  make  twelve  semitones.  Thus 
the  major  second  contains  two  semitones,  conse- 
quently its  inversion  must  contain  ten,  etc.  We 
also  find  tliat  the  inversion  of  a  major  interval  pro- 
duces a  minor,  and  the  reverse  ;  of  an  augmented,  a 
diminished  ;  of  a  perfect,  a  perfect.  Removing  one 
of  the  sounds  of  an  interval  an  octave  does  not 
chiingo  its  name,  except  in  the  cases  to  be  pointed 
out  hereafter,  thus : 


Third. 


Third. 


I 


W^^ 


i 


Both  these  intervals  are  thirds,  or  the  second  example  is  a 
third  plus  an  octave. 

6.  Intervals  are  also  divided  into  consonant  and 
dissonant.  The  consonant  intervals  are  :  The  major 
and  minor  thirds,  and  their  inversions,  the  minor 
and  major  sixths.  The  perfect  fourth  and  its  inver- 
sion, the  perfect  fifth  ;  and  the  octave.  A  conso- 
nant interval  is  One  that  gives  repose  to  the  ear ;  a 
dissonant  interval  does  not ;  but  it  must  be  resolved, 
a  term  that  will  be  explained  in  its  proper  place. 

Before  going  any  further  the  student  must  become  thor- 
oughly familiar  with  all  these  intervals.  This  is  best  done 
by  writing  them  out,  •ommencing  with  every  ti,  #  *nd  t>  in 
the  scale. 

*l.  A  tetrachord  is  a  series  of  four  sounds,  ar- 
ranged as  follows  :  From  first  to  second,  and  second 


I 


an  inttTval 
tones.  Thus 
ones,  conse- 
n,  etc.  We 
interval  pro- 
lUgmonted,  a 
emovlng  one 
,ve  does  not 
o  be  pointed 


d  example  ia  a 

msonnnt  and 
:  The  major 
;,  the  minor 
nd  its  inver- 
!.  A  conso- 
;o  the  ear ;  a 
be  resolved, 
)er  place. 

become  thor- 
B  is  best  done 
fl,  #  and  \>  in 

sounds,  ar- 
,  and  second 


CliARlCE'S    HARMONY. 


11 


to  third,  are  major  seconds  ;  from  third  to  fourth,  a 
minor  second,  thus  :  G,  A,  Bi^C. 

8.   A  major  scale  consists  of  two  ti-trachords  sepa- 
rated by  a  major  second,  tiius  •. 

Tetrachord.  Tetrachord. 


^  I 


==.l^^=:±E~?r:: 


:A: 


-«- 


m 


Separating  whole  tone. 

9.  Every  tetrachord' may  be  found  in  two  scales, 
viz. :  The  scales  of  its  first  and  of  its  last  note. 
Thus  C,  1),  E^F  belongs  to  the  scales  of  C  and  F; 
F,  G,  A,  Bj^  to  the  scales  of  F  ami  B.^. 

10.  Scales  having  tetrachords  in  common  are 
called  related  scales.  Thus  the  scales  of  F  and  G 
are  related  to  C,  because  they  eacli  h  ive  a  tetracliord 
that  also  belongs  to  C  ;  therefore  every  major  scale 
has  two  major  relations,  because  C  is  the  model  for 
all  major  scales. 

Scale  of  G. 


{ 


Scale  of  D. 


Scale  of  C. 


i|^ 


i 


Scale  of  Bh. 

Write  tetrachords,  commencing  with  every  J.  t  and  b,  and 
mark  the  scales  to  which  they  belong.  No  letter  must  be 
repeated  or  omUted  in  any  scale. 


I 


Kfr 


CHAPTER  II. 

1.  A  common  (^horrt  (or  perfect  chord)  consists 
of  three  sounds.  The  lowest  is  the  root;  tlie  re- 
maining sounds  are  the  third  and  fifth  over  that 
root.  The  tiiird  may  he  major  or  minor ;  the  fifth 
muKt  be  perfect.  A  chord  with  a  major  third  is 
called  a  major  chord ;  with  a  minor  third,  a  minor 
chord.  Since  there  are  only  seven  letters  used  in 
music,  it  follows  that  seven  groups  will  make  all  the 
common  chords  tliat  are  possible,  thus  : 

Fifths. —  E,  F,  G,  A,  H,  C,  T). 
Thirds.— C,  D,  E,  F,  0,  A.  B. 
Roots. —  A,     ?>,     C,     D,     E,     F,     G. 

These  groups  may  be  modified  by  ift,  1»,  elc.  For  example, 
the  first  group,  A,  C,  E,  may  be 


etc. ;  but  the  lettert  never  change. 

2.  Six  common  chords  may  lie  written  in  every 
scale.  Three  will  be  major;  three,  minor.  The 
seventh  note  of  the  scale,  called  the  Icaxliini  note, 
cannot  be  used  as  the  root  of  a  chord,  because  the 

fifth  over  it  is  diminished. 

(12) 


W!'"  "I'B 


hord)  consists 
root;  the  re- 
Ifth  over  that 
liiior ;  the  fifth 
major  third  i-; 
third,  a  minor 
letters  used  in 
ill  make  all  the 
s : 

C,  D. 
A.  B. 
F,     G. 

ic.     For  example, 


^ 


ritten  in  every 
I,  minor.  The 
?  leadincf  note, 
rd,  because  the 


Cr-AUKK'S   IIAIIMONY. 


13 


Example : 

1 


i=l-E 


3  15  8  Dim,  fifth. 


H 


Tonh. 


Subdom.  Dom.  I.cacling 

note. 


The  major  chords  are  on  the  first,  fourth  and  fifth  notes  of 
the  scale.  Those  notes  are  called  the  tonic,  siibdo.ni.iant  and 
dominnnt,  and  the  chorda  written  on  them  are  called  by  the 
same  names. 

The  minor  chords  are  on  the  second,  third  and  Mxih  notes 
of  the  scale.  These  notes  are  called  the  super! onic,  n.ediant 
and  submcdiant,  and  the  chords  written  on  them  are  called 
by  the  same  names. 

3.  It  is  easier  to  -write  Buccessioirs  of  chorda  in 
four  parts  (or  for  four  voices)  ;  but  as  tlie  chord 
consists  of  only  tlirc.,  sounds,  it  is  necessary  to 
double  one  of  tlie  members  of  the  chord  to  make  a 
fourtli  part. 

We  will  commence  by  doubling  the  root,  thus: 


1 


i 


C  is  the  root;  it  is  at  the  base  and  doubled  by  the  highest 
voice  or  part. 

4.  A  chord  with  its  root  at  the  base  and  doubled 
in  one  of  the  upper  parts  may  be  written  in  t'.iree 
positions,  called  :  Octave,  tierce  and  quint. 


I 


mm 


sJ  m 


I 


14 


ni.AUKR'S    HARMONY. 


Octave  {He).  Tierce  (3).  Quin/ (5t). 


::ff± 


m 


-«- 


zs^ 


SJS^ 


i 


8e. 

ZJSr. 


5t. 


is: 


m 


Cloit  Harmony. 


Diiperied  Uarmomj. 


In  all  its  posilions  apd  doubling  this  chord  is  etill  tlie 
chord  C,  E,  O. 

This  doubling  might  be  carried  to  any  extent;  but  it  can- 
not niter  the  name  of  the  chord. 

5.  In  writing  a  succession  of  common  chords 
with  their  roots  at  the  base,  the  following  rule  must 
be  observed  :  Never  write  two  chords  in  succession 
in  the  same  position.  If  it  be  desired  to  malie  the 
succession  as  smooth  as  possible,  retain  all  notes 
common  to  two  or  more  chords  in  the  same  part 
(voice),  thus: 

St.       se. 


The  following  examples  are  to  be  written  according  to  these 
-nles,  Tiz. : 

Ist.  The  base  note  is  the  root. 

2d.  The  root  only  is  to  be  doubled. 

3d.  Two  i-hordg  in  the  same  position  must  never  be  written 
in  succession. 

4th.  Make  the  chords  as  oonneoted  as  possible. 


■' 


m  I'OiinMiirnrairmi  - 


At. 


lil 


m 


Harmony. 

■d  is  gtill   the 

t;  but  it  can- 

mon  chords 
ig  rule  must 
11  succession 
to  make  the 
in  all  notes 
e  same  pail 

3.     5t.       8e. 


1 


ording  to  these 


iver  be  written 


CI.ARKE'rt    HARMONY. 


15 


I 


fi.  The  knowledge  gained  must  now  be  applied  to 
the  harmonizing  of  a  melody.  The  following  re- 
marks will  point  out  the  way  to  accomplish  this  : 

(1 )  Every  note  in  the  melody  may  be  the  root,  tiiird 
or  fiftli,  of  some  one  of  the  chords  in  the  scale.  If  it 
be  treated  as  a  root,  tlic  chord  will  be  in  the  octave 
position;  if  as  a  third,  the  chord  will  be  in  the 
tierce  position ;  if  as  a  fifth,  the  chord  will  be  in 
the  quint  position. 


Example: 


6      8         8 


^^^^^ 


-9' 


N.  B. — Two' chords  may  be  written  in  the  8  position  in  suc- 
cession when  the  extreme  parts  move  opposite  ways. 

In  this  example,  C  is  treated  as  the  root  of  the  chord  of  C, 
consequently  it  is  in  the  octave  position ;  D  as  the  fifth  in  the 
chord  of  G,  consequently  it  is  in  the  quint  position  ;  C  as  the 


I 


utitr" 


10 


(!IiARKE'8    HARMONY. 


third  in  tlio  oliortl  of  A,  conaetjuently  it  ia  in  the  lierc.^  pubi- 
lion,  etc. 

(2)  Begin  and  end  with  tlic  tonie  ciiord. 

(3)  After  deciding  on  the  chord  any  givon  note  is 
to  liave,  write  first  of  all  the  root  in  the  bass. 

Ilarmonizo  llio  folla^^ing  plirase  of  melody  in  as  many  ways 
as  possible : 


-e) — g- 


^ 


-1 — ®- 


i 


Three  chords  aro  possible  for  the  first  note,  two  for  the 
B«c-ind,  three  for  the  fourth. 

1  \e  following  melodies  must  be  harmonized  according  to 
fhcao  rules  ;  they  should  oil  bo  transposed  to  all  the  keys  and 
harmonized  over  and  over. 

Note. — The  bass  must  never  proceed  by  long  skips,  it  is 
best  not  to  exceed  u  sixtli. 


i 


^SM5i-|-V^«Tfg,l/a»f."°^ 


m 


E^;^n^^^m^^ 


The  bass  should  never  ascend  or  descend  two  fourths  or 
fifths  in  succession. 


the  tieroj  pubi- 

)ld. 

givi'U  iioto  is 
le  bass. 

in  ts  many  ways 


m 


jlo,  two  for  the 

ed  according  to 
all  tho  keys  and 

long  skips,  it  is 


two  fourths  or 


^mt 


claeke'h  harmony. 


IT 


It  cannot  bo  too  often  repeated  that  common  chnrdu  onli/,  with 
tho  rootM  at  the  base  and  not  doubled,  are  to  be  used  ill  those 
exerciscH 

Examine  each  chord  as  you  write  it,  to  see  if  it  conforms 
to  these  rules  This  is  the  only  way  to  suooooc  a  the  absence 
of  a  leiichcr. 

1  Tho  progression  of  common  cliords  is  perfectly 
free,  tliat  is,  any  two  common  cliords  may  bo  written 
in  Hiicecssion,  but  some  successions  tlo  not  sound  us 
well  as  others.  They  arc  not  to  be  understood  as 
forbidden,  because  the  effect  of  a  progression  dc- 
peiids  altogether  on  the  design  of  the  composer  and 
tho  context 

The  following  rules  might  be  given  for  such  successions : 

Two  /nnjor  chords  whose  roots  are  a  whole  tone  apart  do 
not  sound  well,  except  in  the  following  positions  :  At  No.  1 — 
two  and  three  are  sometimes  used;  four  is  hardly  tolerable; 
five  is  intolerable. 


•i  3  4  6 

Two  minor  chords  whose   roots  are  a  whole  or  half  tone 
apart  are  bad  in  any  position,  except  in  the  passage  ot  No.  2. 


M^:^^^^ 


J::  I, 


18 


CLARKR  H    HARMONY. 


A  minor  chord  followed  by  a  mnjor  whuno  root  in  u  minor 
third  higher,  is  bad  unless  in  the  following  positions: 


(1^ 


::*: 


P 


m 


jBt 


m 


Oood. 


Better. 


A  mi^or  chord,  followed  by  a  minor  or  the  revorHc,  wlioso 
roots  are  a  half  tone  apart,  except  in  the  following  pogitions : 


:t 


i^^fEiE^^ 


(^ 


m 


^ 


^ 


zgiz 


m 


Nos.  1  and  2  are  best. 

8.  It  is  not  always  necessary  to  use  the  root  of  a 
/jhonl  for  a  base  note.  Tlie  third  or  fifth  may  be  so 
nsed.  When  the  third  is  used  for  a  base  note  the , 
chord  is  said  to  l)e  in  Its  Jirst  inversion i  when  tlie 
fifth  is  used  for  a  base  note  the  chord  is  said  to  l)e 
in  its  second  inversion.  It  is  important  to  remem- 
ber that  tlie  name  of  the  chord  is  unchanged,  iio 
matter  what  the  inversion  of  the  letters  composing 
it  m&y  be,  thus : 


s  root  in  II  minor 
isiliona: 


fa 


1 


0  reverHc,  wlioso 
wing  positiuuB : 


-Ol- 


m 


the  root  of  a 
fth  may  be  bo 
base  note  the , 
oiii  when  tlie 

is  said  to  be 
nt  to  rcmem- 
nchanged,  iio 
rs  composing 


CI.ARKR'et    HAKMONV. 


19 


i 


EE^: 


-•- 


i 


In  thift  oiample  the  Ittliri  »re  C,  E,  0 ;  it  la  therefore  the 
chord  of  (.', 

To  And  Iho  mot  of  a  chord  it  is  only  neoensary  to  arrange 
the  lelturs  composing  it,  ao  aa  to  read:  1,  A,  6.  The  loweat 
will  be  the  root. 


Example : 


1 


i 


3 


5         « 


EE^lEllEl^iEi^: 


1    a   6 
No.  1  is  the  chord  of  A,  Ist  inversion,  the  letters  read  A,  C,  E, 
41  2        "       "  Q,  2d  "    with  root  doubled,  0,  D,  D, 

•■   8        "       •'  C,  Ist         "    with  fifth  doubled,  C,  E,  G, 

<i  4        1.       n  F.  2d  "       "       "  "  F.  A,  C, 

•••  6        "       "  D,  Ist         "  *  I>i  fi  A, 

>f  C        "       "  K,  Ist         "    with  fifth  doubled,  E,  0,  B. 

The  pupil  should  write  all  the  common  chords  in  all  the 
keys;  in  nil  their  positions  and  inversions.  Remember  that 
position  applies  to  the  hightst  note  of  a  chord  with  its  root  at 
the  base ;  and  invenion  applies  t  a  chord  with  any  member 
but  the  root  at  the  base,  and  has  no  regard  to  whiit  may  be  at 
the  lop  of  the  chord. 

9,  Hitherto  we  have  doubled  the  root  of  the  chord 
only ;  but  it  in  not  the  only  member  of  the  chord 
that  can  be  doubled,  but  is  the  6e.s<  when  the  root 
is  at  the  b.ase.  But  when  the  first  inversion  of  the 
chord  is  used,  the  fifth  is  just  as  good  a  monibei  to 
double  as  the  root.  (For  the  present  the  third  must 
not  be  doubled). 


I 


II    > 


J 


20 


clahkk'h  iiaumuny. 


In  llie  fnllnwinn  OKtimplc,  tlio  first  inversion  of  iomo  of  tli« 
ehonU  w.ll  lio  foiinil— Honiu  with  root,  nome  with  flftli  doubled. 


N.  D.— The  doubliiiK  of  a  membor  of  a  chonl  nt  uniaon  in 
exprrsHcd  )iy*writing  llio  nolo  ns  above.  It  is  hm  (hough  two 
of  the  gingers  in  a  qiinrtetto  hud  the  game  note  to  sing. 

1,  Chord  of  (',  Ho  position,    lloot  doubled.  Tonlo  chord. 

"         0,  IbI  invcTHion,         "  Doiii. 

C,  Ho  position,            "  Tonic         " 

"        (",  iHlinvcrtdon,         "  "            " 

"         F,  8e  position,            "  Subdoin.     " 

"         D,  1st  invoTHion,         •'  Sup.  tonlo " 

"         G,  8o  position,            "  Dom.          " 

<<         (;_  Ho         "                 "  Tonic         " 

"         F,  1st  inversion,         "  Subdoin.     " 

"        0,  1st         "                "  Dom.          " 

"         r,  3c  position,            "  Tonic         " 

"         0,  1st  invcrHion,  Fifth  doubled,      '•  " 

'<         1),  Ist         "          Root  doubled  Sup.  Icmic  " 

"         l»,  3«  position,            "  "            " 

C,  6t        "                  "  Dom.          " 

•<        C,  3e        "                  "  Tonic         " 

In  writing  the  following  exercises,  it  is  optional  to  molto  the 
notes  cither  roots  or  thirds  of  chords.  Try  both  and  let  (he 
ear  decide.     The  f  .Unvini;  example  will  point  out  llio  way  : 


No. 

1. 

(1 

2. 

II 

n, 

11 

4, 

11 

r., 

(1 

c>. 

11 

">, 

11 

8. 

11 

0. 

*i 

10, 

11 

11, 

11 

12, 

11 

lil, 

11 

14, 

11 

15, 

11 

16, 

1 


it 


■i 


--o — 


i 


;i  of  iomo  of  tli« 
til  flflli  (loubUd. 

'tot  ^<  \ — ^ 

I     IS  14  1A  in 

oril  at  uniHon  in 
U  an  tliough  two 
e  lo  Hing. 

Bil,   Tonic  chord. 
Doni.  " 

Tonic         " 


Siibdoni.  " 
Sup.  tonic  " 
Uom. 

Tonic  " 
Subdoin.  " 
Dom.  " 

Tonic 

\ed,      •• 

led  Sup.  Ionic  " 

Uoni.  " 

Tonlo        " 

ional  to  malco  the 
botli  iind  let  the 
t  out  tlio  way  : 


ci.aukk'h  iiahmonv. 


81 


Thin  i^  I'videnlly  in  ilie  key  "f  «' ;  it  """"t  Hicreloro  liogin  nnd 
•nd  witli  ilie  loniu  cliord 

Tlio  neti.nd  notn  miiy  1>«  root  of  the  chord  of  K.  or  the  third 
of  the  cliord  of  V.     (Try  liolh). 

No.  ;i  cniiiiot  l.o  a  root,  heing  llio  leading  nolo;  II  must 
therefore  ho  iv  third  in  chord  of  tl. 

No   4  may  be  root  of  C,  or  third  of  .V      (Again  try  both) 

No.  5  root  of  A.  or  thirl  of  F.     (Again  try  both). 

No.  0  root  of  F,  or  third  of  U.     (Again  try  both). 

No.  7  root  of  0,  or  iliiid  of  E  (Sou  dinngreoable  progren. 
kloni,  piige  17). 

10.   The  following  rtiUi  muHt  bi-  Htrictl.v  observdJ : 

Never  let  two  \mrU  or  voices  proceed  in  octavt-s 

or  imiis  with  each  other.     (Any  two  parts  mny  bo 

an  octavo  or  llftii  iipart ;  but  not  twice  in  succession;. 


P^ 


^ 


^1^^ 


P=^--'3F^3= 


i^^^^^ 


In  the  first  bar,  the  bans  and  tenor  are  a  fifth  apart  in  the 
fl-st  chord,  f}'  and  also  in  the  second,  ^  \  making  two  fifths  In 
succession  between  the  same  two  yoices.  Abo  the  bass  and 
alto  are  on  octavo  apart  in  both  chords. 

Consecutive  fifths  and  octayes,  lilto  this  example,  only  occur 
when  two  chords  are  written  in  succession  in  the  same  posi- 
tion ;  hence  the  rule  forbidding  it. 

In  the  second  bar,  fifths  occur  twice  in  succession  between 
the  alto  and  soprano. 

In  the  third  bar.  fifths  occur  twice  in  succession  between  the 
tenor  and  alto. 

(Consecutive  or  parallel  fifths  will  be  treated  farther  on). 


I 


Clarke's  harmony. 


15 


i=^ 


^ 


t=f::rt 


f- 


t=r«=t 


-«--p 


£s 


i 


S 


ra   #,^- 


x^ 


^ 


STK 


=  :g=»p:>-cp 


tS>5^ 


i 


w^^ 


^m 


=^^ 


B 


3^^i^^y 


^ 


:^ 


i.^ 


r<S>- 


1 


igE 


p 


iSM 


ep 


f= 


Transpose  these  exercises  into  all  the  keys. 

11.  The  next  step  is  to  use  this  first  inversion 
when  harmonizing  a  melody.  The  following  re- 
marks will  make  it  easy  : 

Every  note  in  the  melody  may  be  the  root,  third 
or  fifth  of  some  chord ;  but  if  it  be  treated  as  the 
third  of  a  chord,  the  first  inversion  cannot  be  used, 
because  it  is  forbidden  as  yet  to  double  the  third. 
If  the  note  in  the  melody  be  treated  as  a  root  or  a 
fifth,  either  the  root  or  the  third  may  be  used  for  a 
base  note. 

1  23  4&  87  8 


± 


W: 


No9.  1  and  8  must  have  the  tonic  chord,  which  will  be  in  the 
octave  position. 

No.  2  may  be  treated  as  root  in  the  chord  ot'  D,  and  mw^- 
have  the  root  or  third  at  the  base ;  or  it  may  be  treated  ns  the 


^ 


m 


:^^ 


m 


iipSi 


first  inversion 
B   following   re- 


!  the  root,  third 
I  treated  as  the 
jannot  be  used, 
ouble  the  third, 
d  as  a  root  or  a 
ly  be  used  for  a 


hich  will  be  in  the 

)rd  ot"  D,  and  ma.*-- 
y  be  treated  os  the 


clabkk's  harmony.  23 

fifth  in  the  chord  of  O,  and  may  have  the  root  or  third  at  the 

base. 

No.  3  may  bo  root  of  E,  third  of  C,  or  fifth  of  A ;  if  treated 
as  third  of  C,  the  root  must  be  at  the  base ;  with  the  other 
two  chords,  either  root  or  third  may  be  at  the  base. 

No.  4  may  be  root  of  F,  or  third  of  D. 

No.  5  may  bo  root  of  D,  or  fifth  of  Q. 

No.  0  same  as  No.  3. 

No.  7  sara  '  as  Nos.  2  and  6. 

(Try  all  these  varieties  itiid  observe  which  sounds  best  j  if 
several  sound  equally  well,  observe  the  different  effects  they 
give). 

The  pupil  should  now  be  able  to  harmonize  the  following 

examples. 

It  will  be  well  to  bear  in  mind  the  following  remark  : 

It  generally  gives  a  better  effect  to  make  the  extreme  parts, 

bass  and  soprano,  move  in  opposite  directions ;  ».  «.,  when  the 

bass  descends,  let  the  soprano  ascend,  and  t'ic«  vena.     This  is 

not  a  rule,  but  only  a  remark. 


^ 


^^ 


-^^ 


L^^lr  r  r  r  1^ 


Note. These  examples,  even  if  well  harmonized,  sound  un- 
satisfactory ;  owing  to  the  wan*  of  the  perfect  cadence,  treated 
in  the  following  chapter. 


I 


!T 


fc^ 


IT 


24 


CliABKK'S   HARMONY. 


12.  We  proceed  now  to  the  use  of  the  secciid  in- 
version of  the  common  cl  ord,  i.  p.,  with  the  lifth  for 
a  base  note.  A  chord  with  its  fifth  at  the  l«vse,  is 
nhcaijs  (witli  two  exceptions  whicli  we  will  ignore 
for  the  present)  a  tonic  chord.  Therefore,  in  tlie 
key  of  C,  with  ths  chords  so  far  at  our  disposal,  the 
only  chord  that  can  be  used  in  its  second  inversion, 
is  the  chord  C,  E,  G.  The  following  rules  must  be 
observed  when  it  is  thus  used  : 

Ist.  It  (the  second  inversion  of  the  tonic)  must 
be  preceded  by  some  chord  belonging  to  the  scale. 
(This  seems  superfluous  at  present,  Init  its  impor- 
tance will  soon  be  seen.) 

2d.  It  must  be  followed  by  its  dominant  (excep- 
tions will  be  pointed  out  in  time. 


-&■ 


^^ 


in 


In  this  example  at  X  ^'^  second  inyersions  of  the  tonio 
chord,  (ho  first  example  is  preceded  by  th^  gubdominant 
chord,  the  second  by  the  supertonic.  (These  are  the  most 
agreeable  to  use  before  this  second  inyersion,  but  any  other 
can  be  used ;  as  was  remarked  before,  it  depends  on  the  de- 
sign of  tlie  composer  and  the  context.) 

The  close  of  this  example  is  wbat  is  termed  a  full  or  perfect 
cadence  It  is  the  way  the  great  majority  of  compositions 
end,  viz.:  with  second  inversion  of  tonic,  followed  by  domi- 
nant with  root  at  the  bass,  followed  by  tonio  in  octave  position. 


, 


11 


the  aecc  iid  in- 
;h  the  fifth  for 
it  the  base,  is 
ve  will  ignore 
jrefore,  in  the 
r  disposal,  the 
ond  inversion, 
rules  must  be 

le  tonic)  must 
g  to  the  scale. 
l)ut  its  impor- 

ninant  (excep- 


X 


f^ 


m 


ions  of  the  tonic 
th^  Bubdominant 
ese  are  the  most 
on,  but  any  other 
epends  on  the  de- 

1  a  full  or  perfect 
r  of  compositions 
ollowed  by  domi- 
Q  octave  position. 


, 


CLARKE'S    HARMONY. 


25 


We  found  that  the  best  note  to  double,  when  the  root  was  at 
the  base,  is  the  root;  when  the  third  is  at  the  base,  either 
root  or  fifth ;  but  wlien  the  fifth  is  at  the  base,  the  best  note 
to  double  is  the  fifih  ;  next,  the  root. 

Every  change  in  the  position  or  inversion  of  a 
chord  gives  a  new  effect  to  the  chord.  The  octave 
position  is  grave,  massive  and  full  of  repose ;  the 
tierce  is  graceful  and  inclined  to  melancholy,  p-.ir- 
ticularly  when  used  as  a  final ;  the  quint  is  bright 
and  eager,  always  indicating  something  to  como. 

With  regard  to  the  use  of  the  different  members 
as  base  note :  A  chord  with  root  at  the  base,  is  like 
a  cone  in  a  state  of  stable  equilibrium ;  witii  its 
third  in  the  base,  in  a  state  of  neutral  equilibrium ; 
with  its  fifth  in  the  base,  in  a  state  of  unstable  equi- 
librium. 

A  careful  study  of  the  following  example  will  enable  tl  e 
pupil  to  write  the  exercises  that  are  appended. 


=^ 


■»^ 


* 
1 


•-©- 


zst 


■-^^ 


s^ 


4:: 


i 


* 


* 


Where  these  marks  if:  are,  the  second  inversion  of  the  tonic 
chord  may  be  used ;  because  No.  1 ,  the  F  preceding,  may  be 
harmonized  by  the  chord  of  F,  or  by  the  first  inversion,  chord 
of  D ;  No.  2,  the  A  preceding,  by  the  chord  of  A,  or  first  in- 
version of  F ;  No.  3,  by  the  same  as  No.  2.  And  in  each  case 
the  note  following  may  be  harmonized  by  the  dominant  chord. 
After  1  and  3  the  root  of  the  dominant  is  at  the  base ;  No.  2 
the  third  of  the  dominant  at  the  base.  The  remaining  notes 
are  to  be  treated  according  to  the  rules  already  given. 
2 


r-ji' 


d6 


Clarke's  harmony. 


: 


The  marks  X  >■>  ^^^  ^'^^  exercise  indicate  the  places  where 
the  second  inyersion  of  the  tonic  may  be  used. 


m 


^e 


?^ 


:fc^ 


-4— L. 


-9- 


X 


X 


^^^^^^^W 


^^^^iTF 


-1 — 1- 


«-•-■ 


:p^ 


1:::?:=^ 


1 


jgg^P^^JF^lpg^Pllif 


13.  We  now  give  an  example  to  illustiatc  how 
this  second  inversion  may  be  used  wlien  harmonizing 
a  melody. 

After  writing  the  exercises  that  follow,  tho  pupil  should 
carefully  go  over  again  from  the  beginning,  and  should  trans, 
pose  all  the  basses  and  melodies  given  into  all  the  major  keys 
and  harmonize  them.  This  is  absolutely  essential  to  tbo  cou)> 
plete  mastery  of  the  subject. 


I 


--»=is: 


m 


p 


ggff 


-» 


1 


* 

3 


8 


At  No.  1  w»  have  a  note  belonging  to  the  tonic  chord,  pre- 
ceded by  a  note  that  may  belong  to  chord  of  D  or  G  ;  it  is  fol- 
lowed by  a  note  belonging  to  the  dominant  chord.  No.  2 
belongs  to  the  tonic  chord,  etc.     No.  3  belongs  to  tho  tonic,  etc. 


)  the  places  where 
id. 


tp:: 


1^ 


X 


'^m 


EfJE^ 


£EF 


illustiatc  how 
en  harmonizing 


tho  pupil  should 

and  should  trans- 

all  the  major  keys 

lential  to  tbo  com- 


m 


* 

3 

0  Jonic  chord,  pre- 

D  or  G  ;  it  is  fol- 

iDt   chord.     No.  2 

[8  to  tho  tonic,  etc. 


clabke's  harmony. 


ST 


In  short,  whenever  we  find  C,  E  or  0  followed  by  0,  B  or  D, 
the  C,  E  or  O  moy  have  the  second  inversion  of  the  tonic,  and 
tho  Q,  D  or  D  the  dominant  chord. 

The  use  of  this  second  inversion  of  tho  tonic  is  tlio  only 
thing  met  with  so  far  that  is  at  all  difficult,  and  a,  little  study 
and  perseverance  will  soon  overcome  it. 


I 


W 


^?lfffCLn[I?^'5^^S5 


k 


T^f^'l^ricJir^-g^ 


14.  The  third  of  a  chord  may  be  doubled  under 
the  following  circumstances : 

1st.  When  the  parts  or  voices  doubling  it  are 
moving  in  opposite  directions. 

2d.  When  two  chords  are  written  in  succession  in 
the  tierce  position. 

3.  The  doubling  that  results  from  slriking  full 
chords  on  the  piano,  organ  or  orchc-stra. 


I! 


'JL-' 


. 


S8 


CLARKB'8  iiahmony. 


No.  1.  The  E  is  doubled  by  the  bass  and  soprano,  the  bnsi 
ascending,  the  soprano  deBcendiDg;  in  the  second  bar  the 
motion  is  reversed. 

No  2.  In  the  first  bar  the  C  is  dpublcd  by  the  soprano  and 
tenor ;  in  the  second  bar  tlie  A  is  doubled  by  the  same  voices ; 
but  in  this  cose  they  proceed  in  the  some  direction.  This  is 
the  only  woy  an  exception  to  the  rule  about  writing  two 
chords  in  the  tierce  position  in  succession  can  occur.  The 
third  is  doubled  to  avoid  tho  oonseotftivo  fifths  and  eighths 
that  would  result  from  doubling  the  root. 

No.  8.  The  harmony  reduced  to  its  simplest  form  is  only 
the  chord  of  C,  tierce;  G,  quint;  D,  tiercj;  A,  quint.  The 
doublings  in  this  case  are  merely  for  the  s  ke  of  fuller  effeot, 
and  the  harmony  is  to  be  judged  as  to  its  correctness  by  re- 
ducing it  to  its  simplest  form,  viz. : 


:g= 


E 


i 


m 


m 


The  same  remark  applies  to  Ibo  pvrolKl  Cflhs  and  octaves 
in  this  last  example. 

Two  chords  in  succession  in  tho  octave  ^nd  quint 
position  sometimes  occur,  when  the  extreme  parts 
move  in  opposite  directions. 


I 


goprano,  tlie  bnsi 
)  second  bar  tho 

f  the  Boprano  and 
'  tho  same  voices  ; 
lircotion.  This  is 
30ut  writing  two 
,  can  occur.  The 
fiftlis  and  eiglitlis 

jlest  form  is  only 
i;  A,  quint.  The 
ke  of  fuller  effect, 
correctness  by  ro- 


l  fifths  and  octaves 

ctavciind  quint 
extreunc  parts    , 


clabke's  harmony. 


99 


^^^^ 


$^ 


i 


No.  1  is  common  in  terminations. 

No.  2  is  an  example  of  consecutive  fifths,  from  the  slow 
movement  of  Beetho'cn's  "First  Symphooy." 

The  second  inversion  of  the  dominant  chord  may  be  used 
M  follows: 


i^^^H^^ 


X 


X 


SI 


^ 


m^ 


It  must  be  preceded  and  followed  by  the  tonic 
chord.'  It  must  never  occur  on  the  accented  part  of 
the  bar.  If  the  tonic  before  it  have  the  root  at  the 
base,  it  must  after  it  have  the  third  at  the  base,  and 
vice  versa. 

This  example  has  two  notes  in  tho  bar,  therefore  only  one 
accent;  if  there  were  four  notes  in  the  bar,  the  third  would 
be  an  accented  note. 

A  subdominant  chord  maj'  be  used  in  its  second 
inversion,  provided  it  is  preceded  and  followed  bj' 
the  toaic,  with  tlie  root  at  the  base. 


80 


CLARKE'S  HARMONY 


* 


^mm^m 


* 


^ 


■.T- 


1 


At  H:  the  Beoond  inversion  of  the  subilominant  occurs;  in 
each  case  it  is  preceded  and  fgllowed  by  the  tonio,  with  its 
root  at  the  base. 


inant  occurs ;  in 
te  tonio,  with  its 


CHAPTER  III. 

1,  The  minor  scale  is  formed  from  the  major,  by 
reananginy  the  notes,  commencing  witli  tlie  sixth. 
It  is  called  the  relative  minor  of  the  major  scale, 
from  which  it  is  formed,  and  has  the  same  signatnro. 

2.  The  most  important  chords  in  the  scale  are  the 
tonic,  siibdominant  and  dominant.  In  the  major 
scale  these  are  all  major  chords.  It  was  found 
(p^ge  12)  that  six  chords  might  be  written  in  every 
scale,  three  major  and  three  minor.  By  rearranging 
the  scale  in  this  way,  the  three  minor  chords  will 
occupy  the  position  formerly  occupied  by  the  three 
major  chords ;  i.  e.,  the  first,  fourth  and  fifth  notes 
of  the  scale,  or  tonic,  subdominant  and  dominant. 


C  maior. 


I 


m 


Sr-^S- 


:«= 


k 


O  major. 


m 


HBMft 


s 


A  minor. 


E  miner. 


^ 


-^f  «  "  "'■tl, 


^^a^^ 


A  is  the  sixth  note  in  C  major.    The  chord,  A,  C,  E,  is  the 
tonic  of  A  minor  and  the  sixth  or  submediant  chord  in  C. 
D,  P,  A,  is  the  subdominant  of  A  or  supertonio  of  C. 
£,  G,  B,  is  the  dominant  of  A  or  mediant  of  C. 
(81) 


I 


JJ' 


J9 


OliABKE'rt  IIARMONV. 


Thin  in  Jho  oldest  foi'm  of  tlie  minor  ncnlc,  nnJ  ooncRpondii 
to  tlio  Qrecli  llypo-Dorian  (or,  according  to  Qlarvanua, 
iColinn) ;  the  major  loalu  being  tlie  Lydian  (or  Ionian,  accord- 
ing to  UlareanuH).  This  form  of  tlic  minor  scale  in  very  Hide 
used  now,  because  it  does  not  admit  of  any  liarmony  but  com- 
mon  ohordc. 

3.  Two  forms  of  minor  scales  are  used  at  present, 
called  the  melodic  and  the  harmonic.  In  the  melodic 
the  sixth  and  seventh  are  raised  in  ascending.  In 
the  harmonic  the  seventh  only  is  raised,  both  ascend- 
ing and  descending.  This  is  the  only  form  with 
which  we  have  to  do  at  present ;  hence  whenc^ver  a 
minor  scale  is  mentioned,  until  further  notice,  it  is 
always  understood  to  have  the  seventh  raised. 


No.  1  is  the  melodic  scale  of  A  minor. 
No.  2  io  the  harmonio  scale  of  A  minor. 

4.  We  have  found  (page  11)  that  every  major 
scale  had  two  major  relations.  It  follows,  since  the 
minor  is  formed  from  the  major,  that  the  relative 
minors  of  these  major  scales  must  also  be  related 
to  the  given  scale,  thus  : 

C  major  has  for  major  relatives,  F  and  G. 

The  relative  minor  of  C  is  A. 

The  relative  minor  of  F  is  D. 

The  relative  minor  of  O  is  E. 
Consequently  we  have  in  every  scale  a  group  of  six 


U 


,  nnd  oorreitpoiidH 
ig  to  Qlar«anu8, 
or  Ionian, acoord- 
Huulo  in  very  111  lie 
liarmony  but  ooui- 


ised  at  present, 
In  the  melodic 
aacending.  In 
id,  both  ascend- 
jnly  form  with 
nee  whenever  n, 
ler  notice,  It  is 
raised. 


it  every  major 
Hows,  isincc  tlio 
lat  tlie  relative 
also  be  related 

F  and  G. 


a  group  of  six 


("I.arkk'h  harmony. 


m 


keys,  Ko  clowly  interwoven  tliat  llioy  cannot  be  iUh- 
nnitfd,  and  we  can  paHH  from  any  one  to  any  ollu-r, 
without  niakinj?  a  permanent  change  of  key  ;  or,  in 
other  words,  any  chord  belonging  to  A  minor,  F  and 
I)  niinor,  (1  and  K  minor,  can  be  nsed  in  the  key  of  C. 

In  all  of  these  minor  keys  the  seventh  must  bo 
raised  to  make  a  leading  note.  Therefore  in  A  minor 
we  will  find  O^;  in  D  mim)r,  C^f;  in  K  minor,  D^. 

Tliereforc  every  raised  note  in  any  given  scale 
Avill  be  a  leading  note  to  some  related  scale.  And 
no  note  in  tlie  scale  (with  one  exception,  to  be  men- 
tioned later)  can  be  raised  unless  it  leads  to  a  re- 
lated scale. 


i 


^pr-^^ 


dfp-^-'^ 


Zo=a^ 


4(0        T     8        W     10     11    13 

1.  Tonic. 

2.  Leading  note  to  D  minor. 
8.  Supertonio. 

4.  Leading  note  to  E  minor. 

6.  Lending  note  to  F  mnjor. 

7.  Leading  note  to  0  mnjor. 
0.  Leading  note  to  A  minor. 

We  SCO  from  this  example  that  a  cbromntic  scale  may  be 
written  in  any  key  without  using  a  sound  foreign  to  its  rela- 
tions, except  in  one  place,  viz.,  the  Clh. 

5.  Four  common  chords  may  bo  written  in  the 

minor  scale. 

8* 


.<u 


Ot.ARKK  rt    riARMnW. 


ri: 


^M. 


=?:^fe-^-iS-ll?_-:!i 


m 


1         'i         3         4         6         «        T        I 

The  lat  ii  lonio. 

The  firth  on  (he  2<1  of  the  icnie  In  diminiRhed. 

The  flflli  on  the  !1J  of  the  Roalo  i«  kugmented,  owing  to  the 
raiving  of  the  lOTentb. 

The  4th  is  the  lubdunilnant. 

The  5th  is  the  dominant.  This  chord  ba«  become  miijor, 
owing  to  the  raising  of  the  leading  note.  This  is  the  only 
chord  that  contains  this  railed  note.  Therefore  we  get  this 
exteusion  to  the  former  rule,  yi*. :  Ererjr  raised  note  In  any 
given  scale  will  be  a  lending  note  to  aoroe  related  scale,  and  it 
tHiml  be  harmon  zed  by  the  dominant  chord  of  Iht  nenle  to  which  it 
leads.  The  mixed  note  or  loading  note  is  the  third  in  the 
dominant  chord. 

The  fitli  chord  is  nii^jor. 

The  fifih  on  the  7:h  of  the  scale  is  diminished. 

(Rules  will  bo  given  in  the  proper  place  for  the  use  of  chords 
with  diminiiihcd  flrths/ 


Ti.  It  will  at  once  l)c  seen  that  tlic  easiest  notes  to 
harinotiizo  in  any  given  base  or  nielodj-,  must  Ik-  the 
notch  raised  by  accidentals ;  1)i  juiisc  tliere  is  onl}' 
one  wa}'  of  liarinoni/.ing  eacli  one. 


1      2^S      4,.^IV      8_7      9^9  lU      11    12    18    14    1ft 


m 


,  owing  to  the 


1)eonme  miijor, 
lis  ia  the  only 
re  we  got  tbii 
ed  note  in  any 
?d  Bcair,  and  it 
»e<il«  to  which  it 
0  third  in  the 


d. 

oufle  of  chord! 

iest  notes  to 

nuiHt  1h>  tlio 

1 10 re  iH  only 


i-\  <5> 


rr 


'^=9- 


m 


•i    IS    14    1ft 


ci.arke'h  harmony. 


86 


No.  1.  Tonic. 

No.  .'.  Uoininanl  of  D  minor. 
No.  n.  Tonlo  of  D  minor. 
No.  4.  Dominant  of  ('. 
No.  Ti,  Tonio  of  C,  flmt  inveriion. 
No.  (1.  Dniiiiimnt  of  A  minor 
No.  7.  Tonio  of  A  minor. 
No.  8.  Dominant  of  0  major. 
No.  0.  Tonio  of  0  mnjor. 
No.  10.  Tonio  of  0  major,  first  inrergion. 
No.  11.  Dominant  of  B  minor.    The  F  mimt  be  »harp,  be- 
oange  E  minor  is  the  relative  of  0,  ond  Q  has  an  F<f, 

No.  12.  Tonlo  of  E  minor. 
'  Nob.  18,  14  and  15.     Chords  in  the  scale. 

It  will  be  observed  that  eyery  one  of  these  uomlnant  chords 
Is  followed  by  its  tonio.  This  is  called  the  first  progression 
(or  resolution)  of  the  dominant  chord,  and  must  bo  for  the 
present  strictly  adhered  to. 

Before  proceeding  to  harmoniie  the  following  exercises,  It 
would  be  well  to  construct  a  few  tables  like  the  accompanying, 
which  will  show  at  a  glance  the  relations  and  the  possible 
accidentals  in  the  given  key. 


rrinoipal  key,  Bl> 
Minor  relations. 
••••G  (leading  note  Fi(). 
D  (leading  note  C#). 


Major  relations. 
F  (leading  note  Et]). 


C  (leading  note  Bt)). 


Et>  (leading  npl^t  D). 


1 


3C 


OLAItKE'S   HARMONY. 


An  eaE>y  wny  to  remember  the  notes  that  may  be  raised,  is  : 
They  are  the  first,  second,  fourth  and  fifth  of  the  scale. 

In  the  exercises  that  follow,  will  be  found  both  basses  and 
melodies,  to  be  harmonized.  There  are  no  neir  rules  as  yet  to 
be  observed ;  but  we  have  made  a  gain  of  four  chords,  viz. : 
The  chords  that  contain  the  accidentals,  which  chords  are  the 
dominants  of  the  related  scales.  These  exercises  mutt  be 
transposed  to  all  the  keys. 


iS^^^^^^^^I^ 


S^^g^^gE^^^^^iLflZpg 


^•-^k=W=^z 


^^^ 


1 


gff|--=77=q^'^=^"=fe=|^^ 


Sp^ 


pz^^— 


m 


9!Ee 


3fc==:^ 


a    ysT    --» 


:pz 


t=T=± 


:p=±=^ 


-®- 


"ZZ — — ^ 


i 


^^^^irfi^^^^m 


X 


may  bn  raised,  is  ; 
of  the  scale. 

nd  both  basses  and 
new  rule?  as  yet  to 
r  four  chords,  viz.  : 
hich  chords  are  the 
exercises  mutt  be 


^^1^8 


i^ 


*^ 


• — *- 


^^ 


r 


'ZZ — — ^ 


i 


^^S 


■^V;- 


clauke's  harmony. 


37 


PlS^^^l^^felpi 


1.  In  addition  to  the  related  scales  there  is  another 
scale  from  which  we  cin  borrow  some  chords,  viz., 
the  parallel  minor.  By  parallel  minor  is  meant  the 
minor  scale  beginning  with  the  same  ke5-note.  Thus 
the  parallel  minor  of  C  major  is  C  minor;  it  has 
three  flats  for  signature,  being  the  relative  minor 
of  El,. 

Rule. In  any  given  major  scale  the  chords  be- 
longing to  its  parallel  minor  may  be  used.  These 
chords  are  three  in  number  (one  being  the  same, 
whether  the  key  is  major  or  mi.i0r,  viz.,  the  dominant). 

C  Major,' 


w^- 


m 


4  6  0 

6  5  6 


*^ 


i|E(6|):4ae^l 


0  minor,  parallel  minor  of  C  major,  and  relative  minor  of  Ey 


I  , 


1j# 


I 


II 


38 


CLARKE'S   HARMONY. 


We  now  have  a  means  to  hnrmoniie  E'c  or  Al>  in  a  malody 
in  the  key  of  C,  viz. :  By  C,  E^  0 ;  F,  A>,  C;  or  A',  C,  E^  ; 
which  laal  chord  includes  botii  these  notes. 

C,  Eb,  0.— Is  generally  used  as  follows,  t.  «.,  preceded  by  the 
major  tonic  or  dominant,  and  followed  by  the  dominant  or 
chord  on  the  sixth  of  parallel  minor. 


^     ( 


^=± 


tfc^Ofa:^ 


^=Tfi= 


F,  Al>,  C. — Preceded  by  the  tonic,  or  major  subdominant,  or 
submediant,  and  followed  by  the  tonic. 


Al»  C,  E'?. Preceded  by  the  tonic  or  dominant,  and  followed 

by  the  tonic  or  dominant. 


^Sg^^^ 


n 
yi 
it 
E 

Bl 

n 
b 


'  Al>  in  a  malody 
1;  or  A',  C,  E^! 


preceded  by  the 
lie  dominant  or 


subdominant,  or 


ifeft 


ant,  and  followed 


fe 


M 


m 


CLARKE'S   IIAEMON'-'.  39 

All  these  chords  are  frequently  used  in  succession,  as  follows: 


'^P- 


-»- 


ffi 


in 


W- 


1 


8.  The  last  common  chord  is  the  chord  of  the 
lowered  supertonic,  which  is  formed  as  follows : 

Rule The  supertonic  of  any  scale,  major  or 

minor,  may  be  lowered,  and  a  major  chord  may  be 
written  on  it.  Thus  the  supertonic  of  C  is  D ;  lowered, 
it  becomes  D^.  The  major  chord  written  on  it  is 
Dj,,  F,  A^. 

This  chord  should  be  preceded  by  the  tonic  or 
subdominant,  or  by  one  of  the  chords  of  the  parallel 
minor,  and  should  be  followed  by  the  dominant,  or 
by  the  second  inversion  of  the  tonic. 

This  chord  is  more  frequently  used  in  its  first  inversion  than 
in  any  other  way ;  and  in  this  form  is  called  the  Neapolitan 
sixth — for  some  unknown  reason ;  and  has  a  strange  account 
gifcn  of  its  derivation.     (See  Grovt't  Diet.,  Neapolitan  tixth). 


I 


40 


CLARKE'S    HARMON',. 


^ 


->- 


7(S> 


f 


-W 


^^^^^ 


-»■    a     g— 


:t=a: 


i 


1,  2  and  8.  First  inrerBion  of  lowered  aupertonic :  preceded 
by  tonic,  major  and  minor;  followed  by  dominant,  or  tonio 
second  inversion. 

4.  The  chord  is  preceded  by  the  chord  on  sixth  of  parallel 
minor,  and  has  the  root  in  the  base. 

6.  Preceded  by  subdominant  of  parallel  minor. 

In  the  following  example  from  Weber  (Der  Freiscliulz),  the 
second  inveri-ion  of  this  chord  is  used,  followed  by  the  dominant. 


^HMLt-rrt^;^ 


^ 


m 


^-f^ 


7±Z± 


^. 


'?^ 


'^. 


m 


^^ag^^^ss 


liiiii 


f 


:f=l 


m 


apei'tonic :  preceded 
dominant,  or  tonio 

on  8islh  of  parallel 

minor, 

Der  FreiNcliuIz),  the 
Ted  by  the  dominant. 


^ 


^M 


irtSi^ig 


P 


^SS 


CtARKE's   HARMONY. 


41 


^^{^^j^I^}^ 


9.  We  return  now  to  the  rule  (on  page  24)  that 
the  second  inversion  of  the  tonic  must  be  preceded 
by  8om,i  chord  belonging  to  its  own  scale.  This 
must  be  now  understood  to  include  all  the  chords 
thus  far  mentioned,  viz.,  the  chords  from  the  parallel 
minor,  the  lowered  supertonic  chord,  and  even  some 
of  the  dominant  chords  of  the  related  keys  ;  but  the 
rule  still  holds  good  that  this  second  inversion  must 
be  followed  by  the  dominant  chord. 


I 
X 


-1- 


r 


^ 


-o — ^ 


X 

1^ 


i 


a 


^^^pr^^ 


I 

X 


^^^^ 


No8  4,  5  and  6  are  not  commonly  msS.  with,  but  can  be  rery 
effective.    These  three  examples  (4,  6  and  C)  areacon-radiction 


I 


42 


clabke'h  harmont. 


or  exception  to  the  rule  (page  86),  that  the  dominant  must  be 
followed  by  (he  tonic.  (The  progresgions  of  the  dominant  will 
be  more  fully  treated  in  the  next  chivplor). 

Another  rule  must  now  be  given,  viz. :  When  a  note  is  altered 
by  an  accidental  it  mast  remsin  in  the  same  part  or  voice  that 
it  had  before  alteration,  thus : 


Bad. 


Oood. 


^mm^ 


O' 

B 
n 
d 


No.  1  is  bad,  because  the  C  is  natural  at  the  one  extreme  of  the 
firt  chord,  and  sharp  at  the  other  extreme  of  the  following 
cliord. 

No.  2  is  good,  because  the  CIK  occurs  in  the  same  part  or 
voice,  vi7.,  the  bass,  that  has  the  Ct]. 

A  passage  like  example  1  is  called  a  cross  or  false  relation. 
It  cnn  occur  sometimes  without  a  bad  effect,  as  will  be  pointed 
out  in  the  proper  place. 


Inminant  must  be 
Ihe  dominant  will 


n  a  note  is  altered 
part  or  voice  that 


ine  extreme  of  the 
of  the  following 

the  same  part  or 


or  false  relation. 
w  will  be  pointed 


CHAPTER  IV. 

• 

1.  The  dominant  cliord  may  have  the  seventh 
over  the  root  added  to  it.  This  seventh  is  minor. 
Being  a  dissonant  interval,  it  must  resolve ;  i.  c, 
move  always  in  one  direction,  viz.,  downwards  one 
degree. 


^- 


-^^<:^=S''-^ 


i 


:^g^^^ 


In  this  example  we  haTe  the  dominant  chord  of  C  with  the 
seventh,  F,  added.  The  voice  or  part  that  has  the  F,  mutt 
afterward  have  E.  J'he  note  to  which  the  seventh  descends, 
is  the  third  of  the  tonic  chord ;  hence  the  rule,  that  the  domi- 
nant must  be  followed  by  the  tonic.  But  there  are  other 
chords  in  the  scale  that  contain  this  resolution  note,  that  may 
be  struck  after  the  dominant.  This  gives  us  three  progres- 
sions for  the  dominant  with  seventh : 

1st.  To  the  tonic  chord. 

2d.  To  the  chord  on  the  sixth  of  the  scale. 

3d.  To  the  dominant  of  the  relative  minor. 

The  first  progression  can  take  place  no  matter  what  the  poii- 
lion  or  invTiion  of  the  two  chords  may  be.  In  this  progres- 
sion the  third  of  the  chord  must  ascend  one  degree. 

(43) 


If 


.44 


CLARKE'S   IIARMONT. 


The  second  progreesion  can  only  take  place  when  the  roof 
of  both  ohordB  are  at  «he  base.  In  this  progression  the  tliird 
may  descend  when  (he  fifth  of  the  chord  is  at  the  top. 

The  third  progression  may  talie  place  no  matter  what  the 
position  or  inversion  of  the  *wo  chords.  In  this  progression 
the  third  does  not  moTC,  because  it  is  the  fifth  of  the  following 
cl  ord.  The  root  mast  be  raised  chromatically  to  the  third  of 
the  following  chord. 

It  is  of  the  greatest  Importance  that  the  pupil  should  fix  in 
his  memory  these  three  progressions  of  the  dominant  chord 
with  sevenths.  The  following  examples  mutt  be  worked  out  in 
every  key. 


^gjjg4— ^"^^ 


i^^^^^^ 


aoe  when  tha  root* 
'ogresBion  the  third 
at  the  top. 
10  matter  what  the 
n  this  progrcsBion 
flh  of  the  following 
sally  to  the  third  of 


pupil  should  fli  in 
lie  dominant  chord 
tit  be  worked  out  in 


»^3?L 


1 


clabke'h  harmony. 


45 


'^E^M^^^^^- 


In  the  above  examples  we  h»Te  CTery  rariety  of  the  first 
progression  of  the  dominant  with  seTcnths. 

No.  1.  AVith  roots  of  both  chords  at  the  base,  and  seTenth, 
fifth  and  third  of  the  dominant  chord  at  Iho  top.  It  will  bo 
seen  from  this  example  that  when  the  roots  of  both  chords  are 
nt  the  base,  the  fifth  of  the  tonic  must  be  omitted,  owing  to 
f-e  progression  of  the  sercnth  and  third  of  the  dominant.  (It 
is  common  in  terminations  to  let  the  third  of  the  dominant 
descend  to  the  fifth  of  the  tonic,  but  it  is  in  questionable  taste.) 

No.  2.  We  have  the  first  inversion  of  the  dominant  with 
setenth  in  all  positions. 

No.  3.  We  have  the  second  inversion  of  the  dominant  with 
seventh  in  all  posiiions.  This  second  inversion  of  the  domi- 
nant is  under  no  restrictions  as  to  its  use  ot  any  time,  owing 
to  the  presence  of  the  seventh.  The  small  notes  in  the  bars 
indicate  that  the  D  ntiy  go  to  C  or  E ;  if  it  takes  the  E,  the 
third  is  doubled ;  but  it  occurs  in  contrary  motion,  and  is  very 
effective,  particularly  when  it  occurs  as  at  X- 

No.  4  is  the  third  inversion  of  this  chord,  viz  ,  with  the  seventh 
for  ft  base  note.  The  small  note  in  the  first  bnr  of  this  example 
shows  how  Iho  third  of  the  tonio  may  bo  doubled  in  contrary 
motion. 

From  these  examples  we  get  the  following  rules  for  iho  first 
progression  of  the  dcaiinant  with  seventh  : 

Ist.  When  the  root  of  the  dominant  is  at  the  base,  the  tonic 
must  hove  its  root  or  fifth  at  the  base ;  never  the  third. 

2d.  When  the  third  of  the  dominant  is  at  the  base,  the  tonio 
mutt  hove  the  root  at  the  base. 


IT 


46 


CLAHKRH   IIAUMUNY. 


8d.  When  (be  flfib  of  the  dominknt  is  at  tb«  baio,  tho  tonic 
muat  have  ib«  root  or  third  (somctimei  tbo  flftb,  but  it  ia  not 
good). 

4(b.  When  the  BeTcnlh  of  the  dominant  is  at  Ike  base,  the 
tonio  mutt  hare  the  third. 

Second  progrciaion  of  dominant  with  seventh  ; 


No.  1.  TbeeeTcnth  iaat  the  top.  The  third  of  tlie  dominant 
muat  ascend.  The  third  of  the  chord  on  the  sixth  niu.H  bo 
doubled,  to  avoid  the  conaeoutive  fifths,  which  would  occur  if 
the  D  were  to  take  the  E. 

No,  2.  The  dominant  has  the  i.  ih  at  the  top.  ,  The  third  in 
this  case  can  either  ascend  or  descend. 

No.  8.  The  dominant  has  the  third  at  the  top,  oonspquently 
the  third  of  the  following  chord  must  be  du  ibled.  (See  rule 
for  writing  two  chcrud  in  tieroe  position).  The  sniall  notes 
at  the  end  of  each  bar  signify  that  the  chord  on  tho  sixth  of 
the  parallel  minor  is  included  in  this  second  progression. 

Example  3  ia  sometimes  followed  by  the  chord  on  the  sixth 
in  tho  octave  position,  but  rarely 


:i^ 


in 


':g^ 


-9- 


i 


t  tb«  baio,  tho  tonic 
no  flftb,  but  it  ia  not 

',  is  at  Ibo  base,  the 


Tentli ; 


^ 


bird  of  tlio  dominant 
1  the  sixth  niu.U  bo 
rhich  would  occur  if 

e  top.  ,  The  third  in 

he  top,  oonspquently 
do  ibled.  (See  rule 
i).  Tlie  sniall  notes 
liord  on  the  sixth  of 
ad  progression. 

le  chord  on  (be  sixth 


OLARKE'H   HARMONY. 
Third  progression  of  dominant  with  sevcntht 


(^tei^^^J 


(^^^^^^^ 


( 


:=li5^5|j> 


'n 


--sQ> 


2! — u — 9- — \--~^ — 9-^—6 


( 


-» 9- 


-9 !»- 


J 1 ^- 


^m 


(P^i^#^#. 


m^^^m 


n 


Iq  thoM  esftmples  are  %\\  tho  vurielios  of  which  Ihij.  pro- 
groosion  ia  oapkbte. 


I 


l^;i%. 


48 


ChARKBH   IIAH>U»NY. 


n  will  bo  »ccn  llmt  ilie  root  of  the  first  chord  alwnyH  ho- 
conici  the  third  of  the  .ccond  (by  the  ohromatio  alicratlon, 
effected  by  the  #).  Thli  !•  In  Moordftnce  with  the  rule  on 
page  42,  Ihnt  wheneter  a  note  Ir  altered  chromaUcnlly  It  niu»t 
remain  in  the  Bame  part  or  Toice  that  it  hiid  previous  lo  alter- 
alinn.  It  will  also  be  accn  that  the  aetenth  alwaya  descends 
one  degree. 

It  is  evident  that  this  third  jirogression  of  the  dominant 
(I.  c,  lo  the  dominant  of  the  relative  minor)  con  only  liiko 
place  in  a  mnjor  key.  This  leuvea  but  two  progressions  for 
Iho  dominant  wilh  seventh  in  a  minor  key,  tIi.,  lo  (he  tonlo 
and  to  the  chord  on  the  siilh. 

(The  author  cannot  insist  too  strongly  on  the  neocusity  of 
becoming  thoroughly  f  iniilin.r  with  these  three  i-.ogrcssions  in 
every  form  and  in  every  key,  before  proceeding  any  further. 
Their  Importance  will  become  more  -ad  more  manifest  as  we 
proceed). 

The  exercises  that  follow  should  be  writtoT  repeatedly  and 
transposed  to  all  the  keys.  A  careful  study  of  this  example 
will  indicate  how  this  new  chord  may  be  used  vthen  harmon- 
ising A  boss  or  melody. 

It  must  first  bo  remarked  that  all  the  dominants  of  the  re- 
lated keys  may  also  have  the  seventh  added,  and  henceforth 
must  not  be  used  without  the  seventh.  We  have  already 
found  that  every  nolo  in  the  soaie  may  be  either  a  root,  third 
or  fifih  (except  the  loading  note,  which  cannot  bo  a  root;  the 
supcrlonic,  which  cannot  be  a  third  ;  the  subdominant,  which 
cannot  be  a  fifth).  We  now  find  thr.t  they  may  nearly  all  be 
sevenths. 


b*  :* 


-f^ — 


m 


No.  1  is  the  seventh  iu  the  dominant  of  the  related  key,  0 


obord  nlwayH  ho- 
romatlo  allcrntion, 
)  with  tba  riilo  on 
omallcnlly  it  muMt 
I  proviouH  lo  alter- 
h  always  d«*oends 

n  of  the  dominant 
lor)  cnn  only  liiUo 
vo  progrcinions  for 
',  Til.,  lo  (he  tonio 


on  the  neocusHy  of 
reo  )>i'ogroi8ion8  in 
leding  ony  further. 
Dore  nianifeijt  as  we 


ito-1  repeatedly  and 
idy  of  this  eiample 
used  i^hen  harmon« 

ominants  of  the  re- 
Icd,  and  henceforth 
We  have  already 
I  either  a  root,  third 
nnot  bo  a  root ;  (ho 
8ubdominan(,  which 
ey  may  nearly  all  be 


1 


f  (ho  related  key,  0 


(;i..vHKi':  H  ii.vu.Mu.xr. 


40 


No.  2  is  the  Hcventh  in  (he  dominant  of  the  relative  minor,  A. 

No,  4  in  the  sevonlh  in  the  dominant  of  the  key. 

No.  5  is  (he  seTenth  in  (he  dominant  of  D  minor,  (ho  rela- 
tive minor  of  F. 

No.  0  is  (he  seventh  in  the  dominant  of  K  minor,  the  rela- 
tive minor  of  0, 

No,  7  lins  (o  be  lowered  to  Ui',  because  C  is  the  dominant  of 
P,  and  ll.>  is  (he  minor  sevenlh  over  C;  .ilso,  11  \n  tliit  in  (lie 
key  of  F.  (This  gives  us  a  means  to  harmonize  D^  if  it  should 
occur  in  a  melody  in  (ho  key  of  C). 

Since  (he  sevondi  always  descends,  it  is  necessary  before 
(readng  a  note  oh  n  sovenlh,  to  observe  that  it  must  be  followed 
by  a  note  one  degree  lower  than  itself. 


Bar  1.  Tonic,  domionnt  of  key,  with  seventh,  followed  by 

Bar  2.  Chord  on  sixth,  followed  by  dominant  of  F,  seventh 
added,  second  inversion. 

Bar  S.  Tonic  of  F,  followed  by  dominant  of  0,  seventh  added, 
first  inversion. 

Bar  4.  Tonio  of  0,  followed  by  dominant  of  A  minor,  sevonth 
added,  first  inversion. 


I 


CliARKE'S    IIABMONY. 


Bar  6.  Tonio  of  A  minor,  followed  by  dominant  of  D  minor, 
Beventh  added,  third  inversion. 

Bar  6.  Tonio  of  D  minor,  first  inversion,  followed  by  same, 
tierce  position. 

Bar  7.  Second  inversion,  tonio,  followed  by  dominant,  with 

seventh  added. 
Bar  8.  Tonio  of  C,  with  fifth  omitted. 


The  same  melody,  with  another  harmony  : 

(I 


Z=^^-'^ 


^s^:e 


m 


W^^^ 


-9 9- 


-9 — ^ 


m 


The  pupil  should  analyze  this  without  difficulty. 

Try  to  find  opportunities  for  all  the  resolutions  of  the  domi- 
nant. 


5iES^^ 


^._f__>_^b^ 


r 


;^^*i 


g 


L,|, 


linant  of  D  minor, 
followed  by  Bame, 
by  dominant,  with 


^ 


m 


BBculty. 

lutions  of  the  domi- 


.-T-^-J-W- 


4- 


m 


Clarke's  harmony. 


51 


^^9 »-q*=g 


?=^:8F=^ 


-i—r-^r 


S 


pi^^jgfiigEgj^^^pgii 


p^^gi 


XT ' * ' ^ 


^^ 


^z=pig=f=ii?ririff_{>_H*->- 


^fer^^ 


±-T-f^ 


m^^^^mm^m: 


f>~0 


■tE^EIE^tS 


F^ 


It: 


m 


-#-i- 


1^ 


^^^H^^il^ 


I 


52 


clyhke's  harmony. 


Note.— It  is  not  necesaary  to  write  a  separate  chord  to  JTery 
note.     If  two  or  more  notes  in  ruooession  are  members  of  the 
eame  chord,  the  chord  need  not  be  written  with  all  of  them. 
Thus :  Not ; 


mm 


I      ! 

2.  When  the  root  of  a  dominant  chord  with  seventh 
's  omitted,  the  remaining  notes  form  what  is  called 
the  chord  of  diminished  fifth  on  the  leading  note. 
It  must  follow  the  rules  for  the  progression  of  the 
dominant,  as  though  the  root  were  present,  except 
when  it  is  used  in  its  first  inversion  (which  is  the 
best  way  to  use  it),  when  the  seventh  may  ascend 
or  descend. 


^=txa^-^«;^^=:«^ 


1         a  8  4 

No.  1.  Dominant  of  D,  with  serenth. 
No.  2.  Same,  with  root  omitted. 
Nos.  3  and  4  are  the  inversions. 
No.  5  is  llie  first  inversion,  with  the  Herenth  ascending. 

There  are  two  exceptions  to  the  rule  that  ibe  seventh  must 
descend : 


BT—J: 


m^ 


chord  to  dvery 
lembers  of  the 
all  of  them. 


with  seventh 
rhat  is  called 
eading  note, 
ession  of  the 
;sent,  except 
(which  is  the 
may  ascend 


^ 


m 


ascending. 

be  seventh  must 


m 


^ 


CLARKE'S  HARMONY. 


68 


No.  1.  The  dominant,  second  inversion,  with  the  scTenth  at 
the  top,  is  preceded  by  the  tonic,  tierce  position,  and  followed 
by  the  tonic,  first  inversion.  This  is  the  only  way  this  pro- 
gression can  take  place. 

Nos.  2  and  B.  The  seventh  is  doubled,  and  one  resolves  and 
tb<>  other  ascends. 

3.  Any  number  of  dominant  chords  with  sevenths 
may  be  written  in  succession,  whose  roots  are  a  fourth 
apart,  ascending,  or  (what  is  the  same  thing)  a  fifth 
apart,  descending.  The  easiest  rule  to  remember 
this  progression  by,  is :  Lower  the  third  of  each 
chord  chromaticall}-,  and  it  will  be  the  seventh  in 
the  following  chord. 


Jtoo/(.— B  E       A  D       Q  C 

In  this  example  the  six  dominant  chords  that  may  be  used 
in  the  Icey  of  C  are  written  in  succession. 

Other  progressions  of  the  dominant  chord  with 
seventh  may  be  met  with  that  cannot  be  brought 
under  any  rule.  They  are  not  common,  and  can  Imj 
better  learned  by  studying  the  works  of  good  writers 
than  bj'  attempting  to  give  rules  for  them. 


5lE 


^^^^^s 


5i:-^^^^Sfe^ 


64 


CLAEKE'S  HARMONY. 


ig^^^}^^^^^^ 


55^^^ 


5S 


:f=3t 


s 


^^^ 


jg^^ 


p 


g^=?= 


=*=F 


^f^^^f=r=g 


^1  I 


m 


%^^=^^2£i^  j  ^  "'"S^^ 


^ 


-f^Vrf^ 


^^ 


je|F 


S 


^^,.ai-i;i 


? 


^ 


i 


^^ 
^^ 


^m 


CHAPTER  V. 

1.  The  ninth  over  the  root  may  be  added  to  the 
dominant  chord.  The  ninth  is  minor  (t.  e., an  octave 
and  a  semitone)  in  minor  keys.  In  major  keys  it 
may  be  major  or  minor,  but  is  naturally  major. 

2.  The  ninth  resolves  like  the  seventh,  by  descend- 
ing one  degree.  The  first  progression  of  the  domi- 
nant only  is  possible  when  the  ninth  is  added,  viz., 
to  the  tonic  chord. 

3.  The  ninth  cannot  be  used  for  a  base  note ;  nor 
can  it  be  written  close  to  or  below  the  root. 

4.  There  are  therefore  only  three  inversions  of 
this  chord. 


56 


CLARKE'S  HARMONY. 


In  (his  example  are  all  the  dominant  chorda  Ihnt  can  occur 
in  C,  with  the  ninth  added. 

No.  1.  Dominant  of  C,  with  m^or  and  minor  ninth. 
No.  2.  Dominant  of  its  relaiite  minor,  A. 
No.  8.  Dominant  of  F,  with  major  and  minor  ninth. 
No.  4.  Dominant  of  its  relative  minor,  D. 
No.  f.  Dominant  of  0,  with  major  and  minor  ninth. 
No.  C.  Dominant  of  its  relative  minor,  E. 
The  small  notes  indicate  Ibe  resolution  of  the  seventh,  ninth 
and  third. 

When  writing  in  four  parts,  it  is  necessary  to  omit 
one  of  the  notes  of  this  chord.  The  best  one  to 
omit  is  tlie  fifth,  or  the  third  or  sevcntii  may  be 
omitted. 

The  following  example  oonUlns  all  the  inversions  and  posi- 
tions of  the  dominant  of  C,  with  seventh  and  ninth. 

The  pupil  should  write  all  the  dominant  chords  in  the  same 
way,  with  mnjor  and  minor  ninth. 


2  3         4 


5 


^IJBZ. 


7~g^'f=s 


TB^'^    6 


^^^^ 


-®^- 


-«x'- 


Ep^ 


i 


'^^^^ 


^ 


9  10 


m 


^-!.»i»:t;i 


Is  Ihnt  ci»n  o«cur 

or  ninth, 
lor  ninth, 
lor  ninth. 
Ihe  geventb,  ninth 

cessary  to  omit 
le  best  one  to 
eventh  may  be 


rersions  and  posi- 

1  ninth. 

ihords  in  the  same 


-jPv.- 


i 


i 
i 


CLARKE'H   UARMONY. 


6t 


Nor.  1,  2,  3  and  4  are  the  yarioua  inversions  of  the  cliord, 
with  all  the  members  present. 

Nob.  5, 0,  7  and  8  .ire  ezamplea  with  the  fifth  or  third  omitted. 

Nos.  0  and  10.  Same,  with  minor  ninth. 

The  pupil  should  try  to  find  more  than  are  here  giren. 

5.  Although  the  seventh  may  be  added  to  the 
dominant  at  any  time,  the  ninth  cannot.  Observa- 
tion of  the  way  it  is  used  by  good  composers  is  the 
only  way  to  learn.  One  rule  might  be  given,  viz. : 
The  ninth  should  not  be  added  when  making  a  per- 
fect cadence,  unless  it  is  done  as  follows  : 


i 


3- 


^ — ^ 


I^IE 


^m^m^ 


The  ninth  is  resolved  before  the  seventh,  by  deseendinK  to 
the  root  of  the  chord. 


J,ij=i 


J    i 


1 — T—^- 


r 


:4i4 


8» 


68 


claukk'h  harmony. 


! 


p 


^:^ 


:a. 


SSTl 


II 


m^^^m 


TT 


An  analysis  of  this  example  will  guide  to  the  best  manner 
of  using  the  ninth  with  the  dominant. 

6.  This  chord  of  dominant  with  ninth  is  mere 
nscd  without  tl.un  with  the  root.  When  the  root  is 
omitted,  the  cliofd  may  have  the  three  progressions 
of  the  dominant. 


Example: 


It^ii 


«■ 


'^- 


\il  prog.        'id. 


ad.  Sd,  bol!t  ciordt  vUh 

ninth,  root  omitted. 


:.m 


When  the  root  is  omitted,  the  remaining  notes 
may  be  inverted  in  any  way ;  but  the  major  ninth  is 
rarely  used  as  a  base  note. 

1.  1  he  succession  of  dominant  chords,  mentioned 
in  the  last  chapter  (page  47),  c  n  talte  place,  with 
the  ninth  added.  It  is  celdom  written  with  the  voois 
r)rcscnt ;  but  if*  common  without  the  root. 


m 


1 


le  best  manner 


inth  is  mere 
n  the  root  is 
progressions 


I,  bol!)  ciordt  viUh 
root  omilled. 

lainin^  notes 
major  ninth  is 


ds,  mentioned 
te  place,  with 
with  the  '\ioi3 
Dot. 


clabke'b  harmony. 


{)» 


Slii^El^ES^Tft 


Rooln—B       K 


f^^mi 


■szrz: 


mt 


I 


No.  1  is  a  succession  of  dominants  with  minor  ninllis,  root 
omitted.    This  is  known  as  the  diminished  seventh  cliord. 

No.  2  is  tlie  same  siicceBsion ;  but  the  alternate  chords  have 
only  the  seventh.  The  chord  of  B!>  major  is  the  lowered  super- 
tonio  of  A,  hence  it  can  be  followed  by  the  dominant  of  A,  na 
above.  « 

The  pupil  should  write  all  these  chords  in  aV  the  keys  and 
in  all  their  inversions. 

When  harmonixing  the  following  exeTciscs,  it  U  po8i>ible, 
whenever  a  dominant  chord  is  used,  to  omit  the  root  and  add 
the  niRlh.  It  will  be  seen  that  the  lowered  notes  in  the  Bcale 
may  all  be  treated  ns  minor  ninths.  We  find  so  far  that  it  ia 
poss'ble  to  have  four  raised  notes  in  ft  scale;  that  they  are 
leading  notes  to  related  scales ;  also,  we  may  have  four  lowered 
notes  in  a  Fcale  which  will  be  ninths  in  the  dominant  chords 
of  the  scale  and  ita  relations  (although  there  are  other  ways 
to  harmonize  the  lowered  notes).  So  the  accidentals,  that  can 
be  harmonixed  in  a  scale,  tlways  occur  in  dominant  ohords, 
or  the  parallel  minor,  or  lowtred  surertonic. 


\n\ 


1 


60 


CI.AHKR'ri   HARMONY. 


Tho  dominant  wltli  minor  ninth  mny  have  tlie  root 
nnd  third  omitted.  Tho  result  is  ivdiminiHlied  tliord 
on  tho  Bccond  de|?rce  of  b  minor  scale,  Tho  same 
remarks,  as  to  invcrrtion  and  progresHion,  apply  to 
this  chord  as  to  tho  diminished  chord  on  tho  leading 
note  in  tho  minor  key.  It  takes  the  place  of  a  super- 
tonic  chord,  and  is  generally  followed  by  tho  second 
Inversion  of  the  tonic. 


^^^f^^P^ 


A  minor. 


C  major. 


••  i 


pr^^rrrmW^^ 


-I — h 


f=bp 


fTVif^  r  ^^^ 


^^^^^^^ 


'i-a; 


have  the  root 
tiniHliod  thonl 
lu.  Tho  same 
iHion,  apply  to 
on  tlio  luading 
Inco  of  ft  Bupcr- 
I'V  tho  second 


^^ 


^^ 


^^ 

i^^ 


] 


ms 


IXABKK'm   IIAIIMONV. 


61 


i 


"PT 


ite 


n^-:^ 


^^mtmm^m^m 


m^mm^^^^^i 


n 


' 
'  1 


I  ! 


aJ^ 


CHAPTER  VI. 

1  The  eleventh  may  be  added  to  the  dominant. 
It  is  perfect;  being  the  perfect  fourth,  removed  hu 
octave.  The  third  mi.Ht  l)e  omitted  when  the  eh'venth 
is  added.  It  resolves,  by  descending  to  tlie  third  of 
tiie  chord.  If  the  ninth  be  present,  it  generally 
descends  to  the  root  at  the  same  time  that  the 
eleventh  descends  to  the  third.  This  chord  may  be 
inverted  in  any  way  (except  the  ninth,  whicli  eam.ot 
he  a  base  note  or  close  to  tlio  root).  In  four-part 
writin{,s  the  fifth,  seventh  or  ninth  may  bo  omitted. 


^^^m^^^^ 


\ 


s^m^s^^m 


The  above  con.ainH  examples  of  the  way  this  chord  i»  gen- 
erally  used  when  (he  root  !•  present. 

2.  Tliis  chord  is  more  often  used  without  the  root. 
The  root  being  omitted,  tlie  •  lord  has  tlie  three 
progressions  of  the  dominant,  and  it  may  be  in- 
verted in  any  way.  The  following  rules  must  be 
observed :  ^^^^ 


II 


>  tho  (lomiimnt. 
rth,  ri'inovi'd  an 
hon  tlie  t'U'Voiith 
g  to  the  third  of 
nt,  it  gi'iicriiUy 
3  time  tliat  the 
\n  clionl  nmy  ho 
th,  whicli  I'tiiniot 
t).  In  four-part 
may  bo  omitted. 


^^m 


f  this  chord  in  gen- 


without  the  root. 
rd  has  tlie  three 
id  it  may  be  in- 
ig  rules  must  be 


n.ARKK's    HARMONY 


«8 


iHt.  IftluM'h'veiith  dfK<t!nds,th4"  llftli  miiHt  n-main 
Htiifioniirv  or  awcond. 

2<1.  It' llu'  I'hvi'iiUi  rcmaiiiH  Htati<niary,  tlie  llflh 
miiMt  tisceiul  one  degroe. 

3d.  Tiio  root  an<l  tliird  being  absent,  tho  seventh 
and  ninth  are  free  to  move  in  any  direction. 

Rkmabk  — It  iH  liolter,  in  K«nerat,  that  the  eleventh  ihoulJ 
bo  he«ril  In  the  preoetling  chord  ;  but  it  ia  not  neociMry. 


3dE^ 


-31]: 


7. 


f 


-»-- 


^^^^^11 


No  1.  DominaDt  of  C,  eleTenth  added,  root  and  third  omitted. 
The  elevenih  desoenda;  the  ninth  also ;  the  fifth  remains. 

No.  2.  Same,  with  minor  ninth. 

No.  8.  Same,  toUowed  by  tonio.  Eleyenth  remaina ;  fifth 
Mcends. 

No.  4.  Same,  with  minor  ninth. 

No.  5.  Same,  followed  by  dominant  of  relative  minor. 

No.  6.  Same,  followed  by  chord  on  sixth. 


64 


clarkk's  harmony. 


No.  7.  First  invergion  of  game  chord,  followed  by  tonic.  The 
seventh,  F,  may  go  to  0,  E  or  C. 

No.  8.  Same  progression,  with  minor  ninth. 

No.  9.  First  inversion,  followed  by  chord  on  sixth. 

No.  10.  First  inversion,  followed  by  dominant  of  relative 
minor. 

No.  11.  Second  inversion,  followed  by  tonic. 

No.  19,.  Second  inversion,  with  minor  ninth. 

No.  13.  Second  inversion,  followed  by  dominant  of  relative 
minor. 

No.  14.  Second  inversion  followed  by  dominant  of  relative  ' 
miror. 

No.  15.  Third  inverHion,  eleventh  and  ninth  resolving  on 
third  and  root  of  the  chord. 

No.  16.  Third  inversion,  followed  by  dominant  of  relative 
minor. 

No.  17.  Third  inversion,  with  minor  ninth,  followed  by 
dominant  of  relative  minor,  with  enharmonic  change  of  Al? 
toG#. 

It  will  be  seen  from  these  exampleei,  that  the  only  chords 
that  can  follow  this  one  are  the  three  that  may  follow  the  domi- 
nant chord  with  iko  seventh ;  hence  this  group  is  considered 
to  oome  from  ^he  dominant,  as  its  root. 

(Harmoni;<)  the  melodies  already  given  over  again,  and  try 
to  introduce  this  new  chord.) 

Uecapitulation  of  the  harmonies  of  the  dominant : 


i 


'^ 


p 


^- 


m 


lit.       'id.       3d.     ith.      6tk. 


Tli'i  1st  group  consists  of  major  third,  perfect  fifth  and  minor 
seventh,  and  is  a  dominant  with  tihe  seventh  added. 


'oUowed  by  tonic.  The 

ninth. 

ord  on  sixth, 
dominant  of  relative 

tonic, 
ninth. 
7  dominant  of  relative 

J  dominant  of  relative  ' 

d  ninth  resolving  on 

dominant  of  relative 

r  ninth,   followed   by 
Tmonic  change  of  Al> 


that  the  only  cliords 
it  may  follow  the  domi- 
lis  group  ia  considered 


n  over  again,  and  try 


le  dominant : 


Wi 


\th.      6lh. 

perfect  fifth  and  minor 
enth  added. 


CliARKE'S  HARMONY. 


65 


The  2d  group  consists  of  minor  third,  diminished  fifth  and 
minor  seventh,  and  is  a  dominant  with  major  ninth  rdded ; 
root  omitted. 

The  3d  group  consists  of  minor  third,  diminished  fifth  nnd 
diminished  seventh,  and  is  a  dominant  with  minor  ninth  added  ; 
root  omitted. 

The  4th  group  consists  of  minor  third,  perfect  fifth  and 
minor  seventh,  nnd  is  a  dominant  with  major  ninth  and 
eleventh  nddcil ;  root  nnd  third  omitted. 

The  61  h  group  is  the  same  as  the  2d ;  consequently  it  may 
be  eitlier  dominant  with  major  ninth  added,  root  omitted,  or 
dominant  with  minor  nintL  and  eleventh  added,  root  and  tliird 

omitted. 

Consequently  the  2d  group  in  the  above  example  may  come 
from  either  G,  the  dominant  of  C,  or  E,  the  dominant  of  its 
relative  minor.  The  5th  group  may  come  from  Bb,  dominant 
of  E!>,  or  G,  the  dominantof  C,  its  relative  minor.  Therefore 
there  are  four  notes  In  common  between  the  dominant  harmony 
of  a  major  key  and  the  dominant  harmony  of  its  relative  minor. 
By  the  enharmonic  change  of  the  minor  ninth  there  arc  five 
notes  in  common,  thus : 


1.  Dominant  of  C,  with  major  ninth. 

2.  Dominant  of  A,  with  minor  ninth  and  eleventh. 


1^ 


1.  Dominant  of  C,  with  minor  ninth. 

2.  Dominant  of  A,  with  minor  ninth  ;  the  A!*  becoming  0». 


'■■■  't 


it 


66 


OI<ABKi:'S  HABMONT. 


3.  It  is  owing  to  this  fact  of  there  being  so  many 
notes  in  common  between  the  two  chords,  that  any 
group,  derived  from  one,  may  be  followed  by  any 
group,  derived  from  the  other. 


lii 


Every  group  in  this  example,  except  tliose  marked  X.  be- 
longs to  eitlier  the  dominant  harmony  of  C  or  of  A  minor. 

(It  is  sometimes  objected  to  this  way  of  treating  these 
chords— That  to  be  consistent,  such  groups  as  the  following 
should  be  treated  as  coming  from  the  dominant,  vii. :  D,  F,  A, 
which  would  bo  the  fifth,  seventh  and  ninth;  or  F.  A,  0,  which 
would  bo  the  seventh,  ninth  and  eleventh.  This  objection  is 
easily  met  as  follows :  There  must  be  a  dissonant  interval  in  a 
chord  or  it  cinnot  be  a  dominant  harmony.  In  all  the  c 
groups  there  is  either  a  minor  or  diminished  •geventli,  «>r  a 
diminished  fifth.  I  would  Bgaiu  say  that  i*,  is  only  for  llio 
sake  of  simplicity  and  system  thnt  the  domimmt  is  treated  ..s 
the  root  of  the«e  chords  ;  not  from  a  belief  that  it  ia  so.) 


i 


4.  The  succession  of  dominant  chords  (see  page 
53)  is  also  p:)ssil>le  wliou  the  eleventh  i^  added,  al- 
though the  third  is  not  present. 


ere  being  so  many 
3  chords,  that  any 
!  followed  by  any 


,  those  marked  X>  ^** 
if  C  or  of  A  minor 

i»ay  of  treating  these 
roups  as  the  following 
ominant,  vii. :  D,  F,  A, 
inth;  or  F,  A,  0,  which 
enth.  This  objection  is 
dissonant  interval  in  a 
armony.  In  all  the  e 
tninished  •seventh,  or  a 
that  i',  is  only  for  tlu 
)  dominint  is  treated  iis 
elii'f  that  ills  so.) 

lit  chords  (see  page 
[eventh  i^  added,  al- 


olarkk'b  harmony. 


6t 


^^^^ 


2.  Dominant  of  C. 

8.  Dominant  of  F.     Bb  is  the  lowered  third  of  the  preceding 

chord. 

5.  Dominant  of  G. 

6.  Dominant  of  C,  with  elerenth. 

7.  Dominant  of  F,  with  eleventh. 

8.  Same,  with  minor  uinth. 


CHAPTER  VII. 

1.  The  supertonic  of  any  key,  major  or  minor, 
may  be  treated  ae  the  root  of  a  harmony  similar  to 
the  dominant  harmony.  The  four  groups  that  may 
be  derived  from  this  harmony  are  always  followed 
by  the  tonic  chord,  which  sounds  bjst  in  its  second 
inversion.  The  dissonant  notes  in  a  supertonic  har- 
mony do  not  require  resolution,  as  in  the  dominant 
harmonies  by  descending:  they  generall}'^  remain 
stationary  (because  the  seventh,  ninth  and  eleventh 
over  the  supertonic  make  this  tonic  chord). 

If  the  second  inversion  of  the  tonic  is  to  follow 
the  supertonic  harmony,  the  latter  should  have  the 
root,  third  or  fifth  for  a  base  note.  If  the  first  in- 
version of  the  tonic  is  to  follow,  the  supertonic  har- 
mony should  have  the  ninth  (minor  is  best)  for  a 
base  note.  If  the  tonic,  with  root  for  a  base,  is  to 
follow,  the  seventh  of  the  supertonic  harmony  should 
be  in  the  base  and  the  root  omitted. 


V  a  w  8  4 


I 

the 

1 
ad( 

1 
(he 

] 
ad( 

] 
adi 

ba 

ad 

ad 


fo 

lo 
is 

a< 

P' 


II. 


major  or  minor, 
irraony  similar  to 
groups  that  may 
always  followed 
i)jst  in  its  second 
a  supertonic  bar- 
in  the  dominant 
generall}'^  remain 
nth  and  eleventh 
!  chord). 

onic  is  to  follow 
should  have  the 
.  If  the  first  in- 
le  supertonic  liar- 
or  is  best)  for  a 
for  a  base,  is  to 
;  harmony  should 


^^ 


\r 


clabkk's  harmony. 


60 


No.  1.  Supertonic  harmony  of  C,    seventh  added,    root  at 
the  base. 

No.  2.  Supertonio  harmony  of  C,  seventh  and  major  ninth 
added,  root  at  the  base. 

No.  3.  Supertonio  harmony  of  C,  seventh  added,  third  at 
the  base. 

No.  4.  Supertonio  harmony  of  C,  seventh  and  major  ninth 
added,  third  at  the  base. 

No.  5.  Supertonio  harmony  of  C,  seventh  and  minor  ninth 
added,  third  at  the  base. 

No.  6.  Supertonio  harmony  of  C,  seventh  added,  fitlh  at  the 
base. 

No.  7.  Supertonio  harmony  of  C,  seventh  and  major  ninth 
added,  fifth  at  the  base. 

No.  8.  Supertonio  harmony  of  C,  seventh  and  minor  ninth 
added,  fitth  at  the  base. 


^^m 


,r 


No.  1.  Supertonio  harmony  of  C,  minor  ninth  at  the  base, 
followed  by  first  inversion,  tonic. 

No.  2.  Supertonic  harmony  of  C,  seventh  at  the  base,  fol- 
lowed by  toni>  .  root  at  the  base.  (In  this  progression  the  E'? 
is  almost  universally  wriiten  Djf.) 

No.  3.  This  is  the  only  way  this  harmony,  with  the  eleventh 
added,  can  be  used,  viz.,  with  the  minor  ninth  and  in  this 
position. 

No.  4.  This  sometimes  ooouis,  the  third  falling  to  the  root 
of  tbe  tonic. 


S    :! 


i ' 


TO 


CLARKK's   IIABMONY. 


The  Bupertonio  harmony  may  bo  written  after  tho  lowered 
supertonio  chord,  as  follows: 


15 


s=^ 


-9 9- 


i 


liil 


NY. 


(ten  after  tho  lowered 


i 


CHAPTER  VIII. 

1.  The  chord  of  augmented  sixth  is  a  dominant 
or  supertonic  harmony  from  root  to  seventh,  or  from 
third  to  minor  ninth,  with  the  fifth  lowered  chro- 
matically. The  easiest  way  to  remember  it,  is :  the 
so-called  root  is  the  minor  sixth  or  minor  second  of 
the  scale.  This  so-called  root  is  the  fifth  of  the 
original  chord  lowered,  and  is,  strictly  speaking, 
only  a  passing  note  between  the  fifth  of  the  chord 
and  the  note  below,  to  which  it  descends.  This 
chord  must  be  followed  by  the  tonic  or  dominant. 


^fej^^^ 


Ist  example.  First  chord  in  the  dominant  of  G,  or  super- 
tonic  harmony  of  C.  Second  chord  is  the  augmented  sixth  on 
lowered  sixth  of  C,  or  lowered  second  of  G.  The  third  chord 
is  tonic  of  G,  or  dominant  of  C.  Fourth  chord  is  tonic  of  C. 
In  this  example  the  root  is  present. 

2d  exaipple.  The  root  is  absent,  the  minor  ninth  present; 
D  being  the  root.  A  is  the  fifth,  which  is  lowered  to  Al»,  and 
is  called  the  root  of  the  augmented  sixth.  The  augmented 
sixth  lies  between  the  Ab  and  F#.  This  chord  may  be  in- 
Terted  in  three  ways.     It  is  not  often  used  in  inTcrsions  how- 

cTer. 

(71) 


!     S 


ii 


CI^ARKE  H   UAKMUNY. 


^f 


Z^SCZ 


ifsr 


-5? 


t^i;^ 


-Ml 


\n  N:.i  1  the  lowered  flTth,  Ai>,  skips  to  the  root. 

iu  )S"  ;    bo  lowered  fifth  aaccndg  to  the  natural  fifth. 

The  Hixtli  degree  in  a  minor  scale  does  not  require 
to  be  lowered  when  writing  an  augmented  sixth  over 
it ;  or,  in  other  words,  the  dominant  chord  in  which 
this  note  is  the  fifth,  requires  an  accidental. 


Root:  B.     F^  is  the  fifth  ;  but  F  is  natural  in  A  minor. 

2.  The  angirentcd  sixth  on  the  sixth  degree  of  a 
minor  scale  may  be  followed  by  the  tonic  of  the 
relative  major.  This  progression  is  best  with  the 
roots  of  both  chords  in  the  base. 


Augmente)}  sixth  oa  sixth  of  A  minor,  followed  by  tonic  of  C, 
the  relative  major. 

This  progre^ion  can  be  explained  by  our  theory  of  the  three 
progressions  of  «  dominant  chord.  The  root  of  the  first  chord 
is  D,  therefore  it  is  only  the  dominant  chord  of  £,  followed  by 
the  chord  on  the  sixth  of  itc  scale. 

(The  flntiot,  illustration  I  know  of  Ih-.s  progression  is  in  the 
introduction  to  "  Faust" — Gouucd.) 


Y. 

m 

the  root, 
le  natural  fifth. 

edocs  not  require 
mentod  sixth  over 
n.t  chord  in  which 
ccidental. 


.lural  in  A  minor. 

!  sixth  degree  of  a 

the  tonic  of  the 

1  is  best  with  tlie 


followed  by  tonic  of  C, 

tar  theory  of  the  three 
root  of  the  first  chord 
lord  of  £,  followed  by 

9  progreaaion  is  in  the 


CLABKK's    IIAHMONY. 


n 


i^m^ 


1 1  ;    — -<-       ^__ 


P"^^ 


¥ 


1     1 


i 


H--^ 


^^M^M 


•«» 


^^ri^^s 


\nr\     :d~T 


No.  1.  Augmented  sixth  on  sixtbdegreeofD  minor,  followed 

by  dominant. 
*  ^     2.  Augmented  sixth  on  sixth  degree  of  F,  or  supertonio 

of  C. 

No.  o    Augmented  sixth  on  sixth  degree  of  C. 

No.  4.    Augmented  sixth  on  sixth  degree  of  G. 

No.  '^■.  Augmented  sixth  on  sixth  degree  of  A  minor. 

No.  o.  Augmented  sixth  on  sixth  degree  of  C.     This  is  the 
only  way  this  inversion  can  be  used  smoothly. 

No  7.  Augmented  sixth,  lowered  supertonic  of  C,  followed 
by  dominant ;  or  dominant  of  C,  with  lowered  fifth,  followed  by 
dominant. 
4 


\) 


/ 


74 


oi.arke'u  iiahmony. 


The  Augmented  lizth  oompletei  the  liit  of  chorda;  what 
fbllow  »re  either  (uepenaiona  or  retardation!.  Introduce  the 
•uginented  sixth  as  often  ae  poieible  in  the  fullowing  example; 
also  the  supertonio  harmony. 


^^^^^^^ 


:rt?Bc:t}ff=j 


^^ggtg-£^^35g 


-^^^^^^^ 


I  . 


lilt  of  chords;  what 
tioni.  Introduo«  the 
i«  fallowing  eiample; 


s^^ai 


it£^^F=f^ 


CHAPTER  IX. 


1.  When  paHsing  from  one  chord  to  nnotlicr,  one 
or  more  of  the  meml)crs  of  the  first  chord  may  Iw 
prok)ngcd  into  the  second  chord;  provided,  they 
afterward  ascend  or  descend  one  degree  to  a  member 
of  the  stoomi  chord.     This  is  jailed  retardation. 

111         '  II ' 

In  the  lit  example  the  U  is  prolonged  from  the  first  chord 
(with  or  without  a  tie),  in  which  it  is  a  member,  into  the  second, 
in  which  it  is  not  a  member.  It  then  resolves,  by  descending 
onp  degree,  to  C,  the  root  of  the  second  chord.  The  prolonged 
D  is  the  retardation.  The  note  C,  on  which  it  resolves,  is  the 
retarded  note.  This  is  therefore  a  retardation  of  the  root  from 
above. 

The  2J  example  is  a  retardation  of  the  root  from  below. 


f 


7  ftrr: 


Ill 


■-V. 


w 


CLARKE  8   IIAkMONY. 


No.  1.  Retardation  of  root  from  Bb)Te  anU  b«low. 

No.  2.  notardaliun  of  third  rrom  above. 

No.  B.  Rolardation  of  third  from  bslow. 

No.  4.  Retardation  of  third  from  above  and  below. 

No.  0.  Retardation  of  third  from  above  and  root  from  below. 

Nu.  0.  Retardation  of  root  and  third  from  above. 

No.  7.  Retardation  of  third  from  above  and  root  from  abov« 
and  below. 

No.  8.  Retardation  of  (Ifth  from  above. 

No.  0.  Retardation  of  fifth  from  below. 

No.  10.  Rclardtlion  of  third  from  above,  root  from  above 
•nd  below   and  fifth  from  above. 

Tho  following  rules  must  be  observccl : 

Ist.  A  retardation  that  renolvos  upward,  must 
ascend  a  semitone,  except  when  the  noto  on  which 
it  resolves  is  tho  third  of  a  chord ;  in  which  case  it 
may  ascend  a  whole  tone ;  or,  !n  other  words,  tho 
root,  third  and  fifth  ra.  be  retarded  from  ?ibove  by 
a  whole  or  half  tone.  Th'i  third  may  bo  retarded 
from  below  by  a  whole  or  half  tono.  Tho  root  and 
fifth  by  a  half  tono  only. 

2d.  The  noto  on  which  the  retardation  resolves, 
must  never  Iw  sounded  dose  to  or  above  the  retarda- 
tion (the  root  >nay  be  sounded  above). 


V. 


lU 


and  b«low. 


». 


B  and  below, 

I  and  root  from  b«low. 

rom  tboT*. 

•  and  root  from  nbovo 


ovo,  root  from  above 


served : 

V09  upward,  must 
the  noto  on  which 
1 ;  in  which  case  it 
1  other  words,  the 
d?d  from  iftbovo  by 
I  raa}'  bo  retarded 
)no.     The  root  anc^. 


tardation  resolves, 
r  above  the  retarda- 
ove). 


1     r 


CLAWtB'H    HARMONV. 


77 


'dM^k 


♦  '    -"~"-|©         4|» 


No.  1.  The  C  and  D  are  Bounded  together. 
No.  '1  li  pouible. 
No  !)  it  bad. 

3d.  The  note  of  resolution  may  be  sounded  at  the 
octave  below. 


I      I 


' —  i     J 


^i^^ 


4th.  All  t^ese  retardations  may  occur  in  any  of 
the  parts  but  the  base.  The  only  one  that  can  occur 
in  this  is  the  retardation  of  the  third  from  above. 


^^&=f^ 


I.I 


fTF 


n 


I 


1 


r^ 


78  CLARKE'S   HARMONY. 

The  following  example  can  be  easily  aaalyied  : 


^S0?^-t 


W- 


J;^! 


P -:jsr\ 


W^- 


z& 


■I-- 


9 


--»-- 


«-- ■ 


i 


^ 


J~6 


-&- 


t==!!^!_t.-; 


ssr 


1 


=g=Tf;^ 


:<sr 


i 


2.   A  retardation  that  resolves  by  descending,  may 
skip  to  tlie  note  below  its  resolution. 


f^^^m 


f  f 


■^ 
I 


A  retardation  that  resolves  by  ascending,  may  skip 
to  tlie  note  above  its  resolution. 


'T 


ES=itFS=ii^ 


^ 


:±=i: 


~o — © 


J- 


1 


Y. 
laljried : 


* 


-«»■ 


H] 


_t- 


231 


1 


£ — e  * 


—I 1 

rl ^- 

II 

— ' — 1 _ 

"tt 

4 

— o — — 1 

^             II 

)y  descending,  may 
on. 


scending,  may  skip 


iiii 


CLARKE  S   HARMONY. 


19 


Either  may  skip  to  some  other  member  of  the  chord 
in  which  they  resolve,  before  going  to  their  note  of 
resolution. 


^  VT^^ 


1 


I— 


^ 


IL 


r 


-^ 


1     r" 


SE?E*i 


rii:^ 


i:-:^ 


^ 


I 


Or  tliey  maj'  skip  to  some  other  member  of  the 
chord  and  return  to  the  retardation. 


r — 


^uJJ 


"1      r- 

I- I 


"1^ 


S 


"Ur 


5E^ 


zitg. 


aLz^^ 


^ 


i 


Or  they  ma.v  skip  to  some  other  member  of  the 
chord,  and  then,  if  a  descending  retardation,  to  the 
note  below,  and  if  an  ascending  retardation,  to  the 
note  above  the  resolution. 


Sitt* 


Hi 


f 


80 


"3^-. 


CLARKE'S    HABMUXV. 


—1 


h© — 


s 


*^r 


E-i 


Ei3E 


i 


•#+•- 


1 


<s--#- 


i 


ft^ 


The  notes  joined  by  the  lines  are  the  retardation  itnd  its 
resohiiion. 

Harmonize  the  following  melodies — Firot  in  the  sopruno, 
then  in  the  slto,  then  in  the  tenor  part;  so  as  to  become 
familiar  with  retardation  in  all  the  parts.  In  (he  first  example 
(he  re(ardations  are  all  marked  wi(h  a  (io.  This  is  not  always 
necessary,  because  a  note  may  bo  turned  into  a  rctardadon 
by  having  two  chords  'vrKten  to  it,  thus  : 

Soprano.  Alto.  Tenor. 


i 


_?£::--■: 


::fzif~ 


:?=p4--P=^ 


y-i  y- -J 


-^:^^- 


::r- 


:^f=T 


Jfliii 


retardation  itnd  its 

r^t  in  the  supruno, 

t;    so  ag  to  become 

In  (he  flrst  example 

This  is  not  always 

into  a  retardation 

Torior. 


^^£, 


--•q  f—s~ 


fc 


c'labke'8  harmony. 
With  the  retanliilions  i-kipping: 


81 


-•- 


-®-T#- 


;^^^£qr=5^=?r-c==:ff 


i^ 


^3g=f— g— #-: 


tE^EE^. 


r»-— #• 


^^^ 


Without  ties: 


t>=:- 


;pil!i§ig 


g^S?s3!^SiE5 


g^pp^^^gj?^^ 


4* 


1 


;Pi 


15* 


t«  "7.j; 


I    li 


CHAPTER  X. 


li 


1.  An  appoggiatura  or  changing  note  is  a  note 
struck  with  a  chord ;  one  degree  above  or  below  one 
of  the  members  of  the  chord.  Its  only  difference 
from  the  retardation  is,  that  it  need  not.be  a  member 
of  the  chord  preceding  the  one  !in  which  it  is  struck. 
All  the  remarks  applying  to  the  retardation,  apply 
to  the  appoggiatura,  viz. : 

If  above  the  root,  third  or  fifth,  they  may  be  a 
whole  tone  ;  if  below,  a  half  tone,  except  below  the 
third,  when  it  may  be  a  whole  tone.  They  may  skip 
in  the  same  way  that  the  retardation  does.  They 
maj'  occur  before  two  members  of  a  chord,  provided 
they  are  a  third  or  sixth  apart. 


■)f  I  ^  ii  M.  I 


n 


^ 


-9- 


r  *f 


s 


B 


iii 


(«2) 


note  is  a  note 
'e  or  below  one 
only  difference 
ot.be  a  member 
ich  it  is  struck, 
ardatiou,  apply 

they  may  be  a 
:cept  below  the 
Thej  may  skip 
)n  does.  They 
chord,  provided 


U 


■f^dL-:^ 


-«- 
-1 — 
HS- 


s 


=*^ 


*^ 


is: 

H — 

-«s>- 


olarke'b  iia»,:.ionv, 


83 


-o- 


f^^i^tep 


Ai  the  *  we  have  'ngle  appoggiaturns,  from  A  to  B ;  at  B 
are  double  appoggiaturas ;  at  C  tbey  skip  to  '.be  note  above  or 
to  the  note  below  their  resolution. 


2.  Appoggiaturas  always  occur  ou  the  accented 
beat  of  the  measure  or  on  the  first  member  of  a 
beat. 

3.  When  these  dissonant  notes  occur  on  tlie  un- 
accented beats  or  on  the  second  member  of  a  beat, 
they  are  called  passing  notes.  There  aro  five  varie- 
ties of  passing  notes. 

1st.  Those  that  enter  by  degrees,  either  diatonic 
or  chromatic. 


-^-J- 


:iU: 


^-=f 


^^^ 


f 


M 


84 


CLABKK'8  habmqny. 


I^^^^^l 


No.  1.  The  pabjing  notes  are  on  the  unaccented  beats. 
No.  2.  The  passing  notes  are  on  the  unaccented  members  of 
the  beats.  ,   -^ 

No.  8.  The  passing  notes  are  chromatic. 

The  diatonic  passing  notes  generally  occur  between 
two  harmonized  notes,  as  in  the  above  examples; 
bv't  sometimes  two  diatonic  notes  in  succession  are 
passing  notes.  This  can  only  occur  as  follows,  viz., 
the  first  note  is  the  root  of  a  chord,  the  last  its  fifth, 
or  the  reverse. 


K^^* 


Sometimes  a  passing  note  and  changing  note  occur 
in  succession,  as  follows  : 


-Tt— '^  — ^     -< 


^1 


scented  beats, 
icented  members  of 


ly  occur  between 
ibovc  exainples; 
in  succession  are 
p  as  follows,  viz., 
the  last  it&  Afth, 


■m 


Clarke's  harmony. 


85 


The  remarks  with  regard  to  retardations  and 
changing  notes  apply  equally  to  passing  notes,  viz, : 
An  ascending  passing  note  may  skip  to  the  note 
above  its  resolution ;  a  descending  passing  note  to 
tlie  note  below  its  resolution.  Also,  the  note  of 
resolution  and  the  passing  note  should  not  be 
sounded  together;  but  the  note  of  resolution  may 
be  sounded  at  the  octave  above  or  octave  below. 
Also,  passing  notes  may  be  doubled  in  thirds  or 
sixths.  They  may  also  l)c  doubled  at  the  octave  by 
parts  moving  in  opposite  directions.  Lastly,  both 
ascending  and  descending  passing  notes  may  skip 
to  another  member  of  the  chord  before  resolving. 


nging  note  occur 


m 


r 


««»! 


8e 


CLARKB'H   HABMONY. 


^^Jri#|l 


a- 


;^ 


^^^^^^mM 


No.  1.  PaSBiBg  note,  skipping  to  note  above. 

No.  2.  Passiog  note,  sklppiog  to  note  below. 

No  3.  Passing  note,  dounlcd  in  thir.ls  an'l  sixths. 

No.  4.  Passing  note,  doubled  in  thirds  and  octaves,  three 

^"no!  6.  Passing  note,  doubled  in  thirds  and  octaves,  three 

^'no.  C.  Passing  note,  douDled  in  thirds  and  octaves,  fo  ir 
parts. 


Appoggiaturas : 
±: 1 

r-f=^-^q 

^t^=f= 

jd=dr-i-f-: 

|^^fe=:3 

.-     K   \ 

9^^—0 : 

■# — ^ 


::p^=sr: 


:?=*: 


^ 


1 


Same,  skipping: 


^gi^^^^^ 


#-#- 


e; 


^^^^^^^ 


y 


*=F*^ 


1 


w. 

1  sixths. 

ind  octaves,  three 

aud  ooloves,  three 

and  octaves,  fo  ir 


-M 


m 


>=* 


^e 


^^a 


^     I 


clarkb'h  harmony. 

Pnssing  nfites.  first  specie'  ; 


87 


bS?^^^^J^ 


^^m^m^^^M 


>Samo ; 


EE^ 


ji^i^fe^^gi^ 


The  second  variety  of  passing,  notes  consii-ts,  in 
striking  after  a  harmonized  note,  the  degree  above 
or  below,  and  returning  to  the  harmonized  note. 


i 


k^E^^A^ 


* 


gg  clabkb's  harmony. 

All  the  remarkB  concerning  the  pvovioJiH  variety, 
apply  to  this  one. 


N.  B. 


m 


No.  1.  Both  the  note.  »bow  .nd  b«low  the  harmoni«ed  note 

are  struck. 

No.  2    Both  the  notes  below  »nd  abore. 

No.  3-  Doubled  in  thirds. 

No  4,  Doubled  in  sixths. 

No.  5.  Doubled  in  thirds,  not«i  abote  and  below.the  Sarmon- 

ized  note. 

The  third  variety  of  lABsing  notes  enter  by  skips ; 
but  are  subject  to  the  same  rules. 


nh 


4- 


1  a  »  * 


V.B. 


(viojiB  variety, 


(_^ — i 


m 


t  barmonized  note 

below.the  Sarmon- 
enter  by  skips ; 


1,1:1 


olakkg'h  harmony. 


89 


No.  1.  B  ia  a  ptiaiag  note,  onterinK  by  ikip.  It  ih  one 
dcgrcu  below  the  note  to  which  it  puHses.  It  is  a  Henillone; 
because  all  notea  of  this  lorl,  whether  pawing,  chanKing  or 
retardations,  niu.'t  be,  if  below  the  root  or  fifth  of  the  chord, 
a  Hcniilonc. 

No.  2.  Same,  skipping  to  note  aboTe. 

No.  .S.  Same,  skipping  downwards. 

No.  4.  Notes  below  and  above. 

No.  C.  Notes  above  and  below. 

No.  0.  Notes  below,  doubled  in  thirds. 

No.  7.  Notes  below,  doubled  in  sixths. 

No.  K.  Delow  and  above,  in  thirds. 

No.  0.  Same,  in  sixths.  ' 

Although,  when  these  notes  are  above  a  harmonized  note, 
(hey  may  be  a  whole  or  half  tone.  Yet  if  naturally  a  hiilf 
tone,  they  cannot  be  changed  to  a  whole  tone:  although,  if  a 
wliule  tone,  they  may  be  changed  to  a  half  tone.  It  is  fur  this 
reason  that,  at  the  places  marked  N.  D.,  the  first  F  is  made 
sharp  and  the  second  natural.  This  first  F#  is  a  passing  note 
to  0;  the  Ft]  is  a  passing  note  above  E.  If  this  passage 
occurred  in  the  key  of  Q,  then  both  the  F's  would  be  sharp. 

Before  treating  of  the  two  remaining  rarieties  of 
passing  notes,  we  will  give  the  following  general 
rule  for  all  the  preceding  varieties  (including  retar- 
dations) : 

The  notes  that  lie  one  degree  on  either  side  of  a 
harmonized  note,  may  be  struck  Jwfore  it,  either  by 
prolongation  from  a  preceding  chord,  or  by  entering 
diatonically,  chromatically  or  by  skip;  provided, 
always,  that  the  dissonant  note,  be  it  a  retarding, 
changing  or  passing  note,  is  followed  by  a  liarmon- 
ized  note ;  which  harmonized  note  may  either  follow 


90 


clarkk'm  harmony. 


immi'dlately  or  may  bo  delayed  by  the  dissonant 
note  if  below,  skipping  to  the  note  above,  and  vire 
versa,  or  skipping  first  to  some  otlicr  menber  of  tl»e 
c'liord, 

TIjo  fourtli  variety  ia  a  variation  or  ornamentation 
of  tlie  first. 

Tlio  following  example!  will  explain  their  uie: 


.      fe:=fc--r=:z.— _::f^= 


I=:=i:r-=^^±U^ 


'P^ 


']m 


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WEBSTER,  N.Y.  14580 

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CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Institute  for  Historical  Microreproductions  /  Institut  Canadian  de  microreproductions  historiques 


-  '  l|!Br--.''!VJ.i'JJi.^"Jtl«'M'>S'J''-^?iftft.tf '!'.'--'?--'; 'M<aAJ4'MJ"!,-;:' ,V;'' 


T 


Wi"^" 


CliARKE'a   HARMONY. 


91 


These  examples  might  be  multiplied  indefinitely ;  but  enough 
are  given  to  explain  the  formation  of  passages  of  this  kind. 
One  of  the  best  places  to  study  their  yarieties,  is  in  the  -works 
of  Handel.     This  variety  can  be  doubled  in  thirds  and  sixths. 

The  fifth  variety  is  called  the  anticipatory  note. 
Its  use  will  be  easily  seen  from  the  following 
examples : 


■n 


^^^t^jg 


r— ^ 


*=* 


i 


f 


^ 


r      -fi 


(- «J ^ p;^ 

r    ^6 


The  last  is  the  almost  universal  termination  of  all 
of  Ilanrlel's  solos,  airs,  songs,  etc. 

Second  variety  : 


m 


^ 


i»  #  i»- 


|,i."  t\^  rgtr  I'gtf-^to^'^ 


Third  variety : 


^^tefegg 


^r 


92 


CLAKKl'a  HAEMONY. 


V-   \J  ^     I  '  t     I      J      ■'!  i  I  *      l^^^i'     I         I         *      ^^^^Bl ■■■•  — I 


P 


IgE^E^^E^ 


^^ 


^i^gi^i^ 


Fourth  yar'.e(y : 


P**- 


^.^1  iUtit^^t^^^sm 


N.  B 


All  varietieB : 


^^^SS^^^ 


If. 


It^E^M 


*-liM-»- 


^r--^- 


1^ 


^^P 


jE^S^ 


m 


.fe^-?^?^ 


p. 


-PlTF 


Jf=«: 


CliARKC's   HARMON  r.  98 


^3E 


-ta^- 


^ii 


^^g^^g^ag^-^^g 


S£=JZ=?=PZ^ 


?^ 


^ 


At  N.  B.  is  the  melodio  miaor  scale,  first  ascending,  then 
descending.  This  is  the  only  way  it  can  be  used,  viz.,  as  pass- 
ing notes. 


or 


^m^ 


i 


^^^^mm 


i 


94 


clahke'h  harmony. 


(^^^^g^i^^t 


l^^^pt 


The  foregoing  are  exampleB  of  the  use  of  U  2  melodic  and 
harmonic  minor  scales,  with  the  diUirent  harmonies. 

No.  1.  Ascending,  with  tonic.     First  is  best. 

ho.  2.  Ascending,  with  dominant.     Both  are  good. 

No.  8.  Ascending,  with  subdominant. 

No.  4.  Descending,  with  tonic.     First  is  best. 

No.  5.  Descending,  with  dominant. 

No.  6.  Descending,  with  subdominant. 

N08.  7  and  8  are  used  at  the  base.  The  skips  of  augmented 
leooBds  in  passagM  Uke  the  »boTe  in  the  base,  being  very  dis- 
agreeable. 


!■     :i 


^fe^pl 


lae  of  \1  3  melodic  and 
It  harmonies. 

is  best. 

oth  are  good. 

;  is  best. 


rhe  skips  of  augmented 
le  has*,  being  very  dis- 


CHAPTER  XI. 

We  have  now  acquired  all  the  means  of  harmony, 
except  a  few  irregular  or  rare  progressions  and  some 
other  matters  that  would  not  come  in  well  under  any 
of  the  headings  so  far.  This  chapter  will  be  devoted 
to  all  these  matters. 

1.  Pedal  Point — The  tonic  or  dominant,  or  botli, 
may  be  held  for  an  indefinite  time,  and  any  succcs- 
sion  of  harmonies  belonging  to  the  key,  may  be 
written  with  them ;  provided,  the  prolonged  note  is 
a  member  of  the  first  and  last  chord  in  the  series. 
This  prolonged  note  may  have  a  place  in  any  of  the 
parts ;  but  is  more  often  used  as  a  base  note.  The 
harmonies  written  with  a  pedal  note  should  progress 
as  though  the  pedal  note  were  absent.  (It  is  better, 
as  a  general  rule,  that  no  harmonies  more  remote 
than  the  dominant  harmonies  of  the  related  keys  be 
used.) 


I 


'1  I 


96 


CLARKE'8   HARMONY. 


^-^_-J— ._ 


^mi 


\ , — .« — -I 


The  pcd«l  point  is  often  of  very  short  duration,  as  in  tlie 
following  example!: 


-r 


^^ 


^^ 


^IHE 


I     I 


yiAA 


iwF^E^m. 


j-^ 


»_z-i 


^^ 


2.  Exceptional  progressions  of  the  dominant  with 
seventh. 


m 


frrt 


j^ 


rt  duration,  a8  in  tho 


^mm 


«ai 


r  the  dominant  with 


P 

m 


CI.AUKK  h    IIARMU.W. 


97 


In  this  example  Ibo  dominant  ia  followed  by  llicHutidominunl, 
firHt  in-crsion.  The  seventh  does  not  resolve.  This  progros- 
aion  can  occur  both  in  major  nnd  minor  keys. 


(P^; 


— e, a- 


.iii^ss 


1 


In  this  example  the  dcmiuaut  is  followed  by  the  beoond  in- 
version of  the  f  upertonic.  (Properly  consider*.!,  the  whole 
passage  is  dominant  harmony  ;  the  A— A  being  merely  passing 
notes,  doubled  at  (he  octave,  by  two  parts  prooefding  in  oppo- 
site directions  ) 

The  following  progressions  of  the  dominant  with  seventh 
will  sometimes  be  found,  but  are  rare  : 


^     9 


The  following  progroision  of  the  seventh  sometimes  occurs 
when  the  bass  descends  to  (he  third  of  the  tonic.  This  is  done 
to  avoid  the  doubling  of  the  third  in  direct  motion. 


(P^pi 


^^=^11 


;;«' 


<i-iai'~-r-y>i^:^f^irt?'^  i^-jp*Jtwr*r«^;* 


■^ 


9e 


ci.arkk's  harmony. 


8.  The  fifth  of  a  major  chord  may  be  cimngcd  to 
an  augmented  fifth,  provided  the  augmented  fifth 
ascends  one  degree.  (This  applies  also  to  a  domi- 
nant with  seventh.) 


^^^^^^^m 


^t=M.j:T^^^^  II  7^£^ 


1^^ 


No.  1.  The  pecond  chord  is  a  combination  of  .pasBlag  note  E 
and  augmented  fifth,  C^. 


1  A'- 


This  example  is  a  combination  of  a  doub'e  retardation  and  a 
changing  note.  Such  combinations  are  only  possible  when  the 
dissonant  notes,  taken  collectively,  form  part  of  the  dominant 
harmony  of  the  key  of  which  the  chord  on  which  they  resoWe 
ia  the  tonic.  In  this  example,  C#,  E,  Q,  are  part  of  the  domi- 
nant harmony  of  D.  D,  F,  A,  is  the  chord  in  which  these 
notes  resolve. 


lY. 


nay  be  cimnged  to 
10  augmented  fifth 
ics  also  to  a  domi- 


ition  of  .passiag  note  E 


i 


DuVe  retardation  and  a 
only  possible  when  the 
n  part  of  the  dominant 
1  on  which  they  resolve 
,  are  part  of  the  domi- 
chord  in  which  these 


CLARKE'S   IIAKMONY. 


00 


S.  CImnpinf,'  and  pnHsinjr  notoH  may  hv  donhlcd 
when  they  are  ai»  aiigmcutt'd  fourth  or  diminiHiicd 
fifth  apart ;  provided,  the  two  sounds  nlwnys  move 
in  opposite  directions  to  tlicir  resolution. 


11^ 


Passages  like  this  may  be  explained  on  the  theory  of  a 
"  harmony  within  a  harmony ;  "  boonuso  they  always  boar  the 
relation  of  either  dominant  or  supertunio  harmony  to  the  chord 
with  which  they  occur. 


6.  Passages  like  the  following  can  be  used,  con- 
sisting of  passing  notes  of  various  kinds.  The 
design  of  such  pnssages  seems  to  take  possession  of 
the  listener  and  cover  the  harshness  of  the  numerous 
dissonances. 


100 


CI.ABKE'a   UABMONY. 


i^^^idiBlfe 


Tlu'y  in^^*-  «i'wayH  begin  and  oml  with  ii  cliord. 


Vr.rlouH  pnwageH  of  tliis  kind  can  bo  found ;  but  enough 
has  been  taid  to  guide  lo  their  underglanding. 


7.  False  Relation.— Wlien  a  note,  occurring  ui 
two  Buccessivo  chords,  is  chromatically  changed, 
without  remaining  in  the  Hamc  voice,  it  is  termed  a 
false  or  cross  relation. 


^^PU^ 


i 


^^ 


hi 


m^^mm^ 


No.  1  is  always  b«d. 

No».  2,  .S,  4  and  ">  are  common. 


Ii 


IB   I. 


ir. 


iU^ 


tl  with  a  chord. 

10  found ;  but  enough 
iding. 

note,  occurring  141 
natically  changed, 
oice,  it  is  termed  a 


:^™ii 


■*•. 


r^ 


«f 


CLARKE  H    HARMONY. 


101 


Tli«  fullnwin^  niiglit  l>e  firiven  ana  rule  fur  tlioio  progmidonit: 
A  fitUo  relntion  iiiunI  iipvvr  bo  niailo  with  llio  third  of  the  chonl 
(Exaiu|ilo  1) ;  but  it  iiiuy  ocnur  with  nny  ollinr  inoinbor.  Kx- 
tniple  2,  It  Ik  the  seventh  ;  thi'  iinigrcNHion  iit  r^re.  Einmplo 
R  and  4,  It  '\n  the  rooi  thiit  ir  'ored  ;  8  ii  Itetler  than  -1.  Kx- 
an.ple  T),  the  fifth  Ih  altered  :  tKix  is  very  coiiiinon  and  Ih  alwayH 
good. 

8.  Wlien  liny  two  parts  ascend  or  descend  togetlier 
to  an  octave,  from  some  other  interval,  it  is  called  a 
concealed  octave  : 


^ 


m 


Iwcause,  if  tlie  intervening  notes  are  pnt  in  as  in  this 
example,  two  ootavcH  will  rosnlt.  The  unpleasant 
effect  is  supposed  to  be  obliterated  when  the  npper 
part  moves  a  semitone,  as  in  this  example. 

A  fifth,  which  enters  in  this  way,  is  also  called  a 
concealed  fifth. 


I 


ES^ 


:±3= 


t^ 


9.  When  the  different  notes  forming  a  harmony 
are  struck  successively,  instead  of  simultaneously, 
the  chord  is  said  to  be  broken  or  disj^ersed. 


t\ 


r5»T 


!|! 


102  CliABKE's   HARMONY. 

The  following  are  the  commonest  forms  of  d'spersion : 


i"->  r  f  r  >  r  r  -^ 


No.  1  is  called  an  arpeggio. 

Nu   2  bus  no  distinctiTO  name. 

No.  3  is  called  an  "  Alberti  bass,"  from  lis  reputed  inTentor, 
Dominico  Albert!.  Of  conrse,  this  dispersion  may  be  varied 
'n  many  ways.  It  may  also  have  passing  notes  interspersed 
with  the  members  of  the  chord. 


I 


X     X 


XXX 


^^ 


^ 


■¥^ 


^ 


m 


XX       X 


X  X 


^1^ 


-^ 


f  f  f\  tU 


^ 


^ 


These  and  many  other  forms  ore  frequently  met  with,  par- 
ticularly in  modern  piano  music. 


Consecutive  fifths  and  octaves  may  occur  between 
a  part  or  voice  and  tlie  dispor.5ed  notes  of  the  accom- 
panying chord  ;  also,  consecutive  dissonances. 


IS  of  d'spersion : 


n"TT — 


y^^^^ 


P 


n  Its  reputed  inventor, 
persion  may  be  varied 
ing  notes  interspersed 


X        X 


^^ 


^ 


m 


quently  met  with,  par- 


may  occur  between 
notes  of  the  accora- 
dissonances. 


m 


A 


CLARKE  S   HARMONY. 
B  O 


lOS 


-• — I- 


ISIJ 


-'^ 


i 


At  A  there  are  two  fifths;  at  B,  two  octaves;  at  C,  two 
sevenths.  But  the  ear  does  not  recognize  them,  because  it  is 
at  once  satisfied  that  the  harmony  is  as  follo'vs : 


dispersed  or  broken,  for  the  salce  of  variety. 

10.  Concerning  Consecutive  Fifths. — There  is  an 
unfortun.ate  prejudice  against  consecutive  fifths  in 
the  minds  of  the  majority  of  musicians,  in  spite  of 
the  fact  that  they  are  often  used  by  the  greatest 
writers.  The  excuse  given  for  this  is,  tb^t  these 
writers  knew  how  to  use  them.  If  this  is  true,  it 
would  seem  to  be  the  duty  of  any  who  attempts  to 
teach  harmony-  or  composition,  to  find  out  and  formu- 
late the  riilcb  by  wiiich  these  composers  worked. 
The  following  remarks  are  an  attempt  to  supplj- 
some  sucu  rules : 

1st.  Two  perfect  fifths,  occurring  between  extreme 
parts,  arc  alwajs  disagreeable  when  the  roots  are 
within  one  degree  of  each  other.     The  disagreeable 


104 


oi.arke's  harmony. 


effect  is  ii  little  less  when  the  root>(  nre  a  third  apart; 
still  loss,  if  a  fourth  apai-t;  and  least  of  all,  when  a 
fifth  apart.  In  the  last  two  eases  the  softening  of 
tlie  effect  is  owi-ig,  probably,  to  tlic  fnct  that  there 
is  a  connecting  sound,  \'\/..  : 


©- 


-»-• 


m 


It  will  be  seen  that  the  connection  in  tlie  second  example  is 
still  closer  than  in  the  first.  These  two  cases  are  to  be  foond 
in  tlie  works  of  many  good  writers.  Of  course,  the  effect  is 
still  more  softened  by  contrary  motion  between  the  extreme 
parts.     (Seo  example  on  page  29.) 

It  is  possible  to  have  two  perfect  fifths,  in  succession,  between 
the  extreme  parts,  when  one  of  them  occurs  between  any  two 
members  of  the  chord  but  the  root  and  fifth. 


The  first  fifth  is  between  the  root  and  fifth  of  the  chord ;  the 
second,  between  the  fifth  and  seventh  of  the  chord.  (The  absence 
of  unpleasant  effect  here  may  be  owing  to  the  fact  that  it  is 
the  dominant  of  a  minor  key,  followed  by  the  dominant  of  its 
relative  major,  and  these  two  chords  having  so  many  sounds 
in  common.) 


2d.  Two  perfect  fifths,  in  succession,  may  occur 
between  the  middle  parts  (tenor  and  alto),  as  follows: 


nro  !i  third  apart; 
sast  of  all,  when  a 
s  the  softening  of 
lie  fiict  that  there 


1 


,he  second  esnmple  in 
CAses  are  to  be  found 
r  course,  the  effect  is 
between  the  extreme 


in  succession,  between 
curs  between  any  two 
ftli. 


Rfth  of  the  chord ;  the 
ic  chord.  (The  absence 
;  to  the  fact  that  it  is 
iy  the  dominant  of  its 
nvin;;  so  many  sounds 


session,  may  occur 
1(1  alto),  as  follows: 


clarke'8  harmony. 


105 


■without  any  unpleasant  effect.  Of  course,  if  they 
can  occur  at  the  distance  of  fourth  or  fifth  between 
the  extremes,  they  can  between  the  minor  parts  do 
likewise.  They  may  even  occur  a  third  apart,  with- 
out any  serious  unpleasantness. 


T==^ 


1 


3d.  Perfect  fifths,  one  degree  apart,  may  occur 
between  the  base  and  the  tenor  or  alto,  when  they 
result  from  the  resolution  of  nn  augmented  sixth 
chord,  as  follows : 


(This  can  be  found  in  Moiart  and  Beethoven.) 
4th.  Perfect  fifths,  a  third  apart,may  occur  between 
the  base  and  tenor  or  alto,  as  follows : 


m 


-»- 


^ — S^ — If 


5» 


•rrr^ 


111 


lOf) 


OLARKErt    HARMONY. 


5th.  Of  course,  they  may  be  a  fourth  and  fifth 
apart. 

Otij.  A  diminished   can  always  follow  a   perfect 
fifth,  in  a  descending  passage,  as  follows  : 


-»- 


The  perfect  may  follow  the  diminished,  as  follows : 


S 


:f: 


iT 


i 


I  do  not  put  forth  any  of  these  remarks  ns  rules  (except  the 
last,  which  is  old) ;  but  merely  to  point  out  the  way  that  con- 
secutive fifths  are  often  need  by  good  writers.  No  satisfactory 
reason  has  ever  been  given,  why  they  should  be  unpleasant. 
Indeed,  thern  is  good  ground  for  suspicion  that  it  is  merely 
the  result  of  education  ;  the  learner  being  from  the  beginning 
cautioned  against  tliem  as  the  unpardonable  sin'  in  writing. 
(See  Helmholz  and  Pole  on  this  subject.) 

If  the  deciphering  of  old  manuscripts  is  ^o  be  trusted,  there 
was  a  time  when  the  only  intervals  used  were  the  perfect 
fourth  and  fifth  as  follows : 


P^^ 


This  was  known  at  diaphony.  It  may  be  that  the  forbidding 
of  consecutive  fifths,  altogether,  was  merely  a  reaction  from 
this  unquestionably  barbarous  style  of  oompoaition. 


ill|i  « 


J 


rourth  and  fifth 


bllow  a   perfect 
lows : 


shed,  as  follows : 


118  rules  (except  the 
t  the  way  that  con- 
's. No  satisfactory 
uld  be  unpleasant, 
n  that  it  is  merely 
from  the  beginning 
ible  sin'  in  writing. 

^0  be  trusted,  there 
I  were  the  perfect 


that  the  forbidding 
ly  a  reaction  from 
position. 


CHAPTER  XII. 

Suspended  Dissonances  and  Sequences. — Before 
it  was  discovered  that  the  seventh  could  at  any  time 
be  struck  with  the  dominant  chord,  il;  was  used  only 
as  a  suspension  and  coutd  be  added  to  any  chord ; 
but  it  was  and  is  necessary  to  prepare  it ;  i.  e.,  it 
must  be  heard  as  a  member  of  the  preceding  chord. 
The  modern  or  harmonic  system  has  retained  this 
rule  from  the  old  or  contrapuntal  system  ;  therefore 
the  seventh  and  the  ninth  may  be  added  to  any 
chord,  major  or  minor,  by  suspension.  It  must 
always  resolve  like  the  seventh  and  ninth  in  the 
dominant  chord  ;  and  a  chord  with  seventh  or  ninth 
added  by  suspension,  has  three  progressions,  just  as 
the  dominant  chord  has,  viz. :  It  can  be  followed  by 
a  chord  whose  root  is  a  fourth  above  (tonic) ;  a 
second  above  (chord  on  sixth),  and  a  third  below 
(dominant  of  relative  minor). 

Preparation.    Su$peniton.    SeioluHon. 


i 


s 


? 


i 


Si 


^ 


X  1 

(107) 


,1  ■ 


108 


oi.abkk'8  harmony. 


Chord  of  £,  with  auspendeil  seTentli ;  tlio  seTenih  resoWes 
on  C ;  and 

The  chord  marked  1,  in  Rimilar  to  first  progression  of  domi- 
nant with  Hcvcnth. 

The  chord  marked  2,  is  Kimilar  to  second  progression  of 
dominant  with  seventh. 

The  chord  marked  3,  is  similar  to  third  progression  of  domi- 
nant with  seventh. 

Tlie  seventh  and  the  ninth  are  the  onl}'  suspensions 
possihlc.  Tliey  can  be  inverted  like  the  dominant 
with  Bcventii  and  ninth,  in  short  fliords  with  a  sus- 
pended seventh  or  ninth,  arc  in  every  respect  to  be 
treated  just  the  mnie  as  dominant  chords  with 
seventh  or  nintii. 


It  will  be  seen  that  a  suspension  differs  materiallj' 
from  a  retardation,  because  it  always  resolves  down- 
wanly  and  never  w  the  same  chord  in  which  it 
occurs.  Suspensions  may  skip  to  the  note  below 
their  resolution,  or  to  some  other  member  of  the 
chord.  They  are  also  frequently  ornamented  by 
passing  notes. 


•^M^ 


tlio  seTenih  resolves 

progression  of  domi- 

iieooni)  progression  of 

i  progression  of  domi- 

ic  onl}'  suspensions 
like  the  dominant 
fhords  with  a  sns- 
v^ery  respect  to  be 
nant  chords   with 


f 


1  differs  material!}' 
ays  resolves  doicn- 
■hord  in  which  it 
o  the  note  below 
er  member  of  the 
y   ornamented   by 


-|»-^^^.=J 


ci.arke's  uarmony. 


109 


-.-=&=^-Jt^. 


-'z^Er=is-. 


»- 


P=i::p=ft 


z^ 


!  I     I 


5^^^^ 


— -_:rfi: 


m 


This  example  is  founded  on  the  following  suocossion  of  bus- 
pended  sevenths : 


(i 


3tf!^at; 


5=^ 


-t — '— f 


\^m\^^i^^m 


(^^^^i^e^^ 


Sequences. — A  molodic  sequence  consists  of  the 
same  phrase  repeated  at  equidistant  degrees,  thus  : 


i^'^^Ee^ 


m=f^^^^=^f&?^^^ 


A  harmonic  sequence  consists  of  a  series  of  domi- 
nant and  tonic  harmonies  (general!}),  or  augment od 
sixtli  and  tonic  or  dominant  liarmonies ;  tlio  roots 
of  wliich  proceed  by  similar  step?!. 


[iJI 


110 


CLAR»'B'8   HARMONY. 


:i^¥3^:£f^ 


^1 


|^^t^_^^3^^ 


,is=?= 


EE^ 


-®- 


^ 


i 


(1^^ 


1 


s^ 


^^^ 


No.  1  is  a  sequence  of  dominant  and  tonic  chords ;  the  tooU 
fall  a  fifth  and  rise  a  sixth  alternately. 

No.  2  is  a  sequence  of  augmented  sixths  and  dominant  chords. 

the  roots  falling  »  semitone.  ..-»»,»,     Ti,« 

No.  3  contains  both  these  examples  in  the  first  bar  ine 
second  bar  is  a  repetition  of  the  whole  phrase,  one  degree 
higher. 

It  would  be  impossible  to  giye  examples  of  all  the  harmonic 
sequences  that  might  be^made.  The  above  examples  are 
enough  to  explain  the  manner  of  their  construction. 


11(1 ; 


m 


^ 


m 


i^^^3E 


m 


tonic  chords ;  the  toots 

lis  and  dominant  chords, 

1  in  the  first  bar.  The 
lole  phrase,  one  degree 

pies  of  all  the  hannonio 
le  above  examples  are 
■  construction. 


CLARK  E'h    HAHMONY. 


Ill 


Tlic  contrapuntal  Heqncncc  consists  of  ii  sucws- 
sion  of  common  chords,  with  roots  moving  in  some 
regular  i)lan.  Tho  diminished  chords  cm  be  used, 
with  tlic  h)we.st  note  of  tiie  group  for  a  base  note, 
nltliouffli  tliore  is  a  rule  the  eontrary  (see  page  52). 
Tliis  permission  is  for  the  sake  of  preserving  the 
form  of  the  sequence. 


fpf^fp^m^^ 


^^^^^r^^=Ffl£^^'_UJ'-iJt 


No.  1  is  one  of  the  commonest.    The  roots  rise  a  fourth  and 
fell  a  third. 
No.  2.  Roots  rise  a  fifth  and  fall  a  fourth. 
No.  8.  Roots  fall  a  fifth  and  rise  a  fourth. 


112  OLARKR'H    HARMONY. 

No.  4  oon.i.t»  of  a  phmHO  of  four  chord.,  toreated  a  third 
lower. 

No..  1,  a  and  4  can  l.o  changed  into  harmonic  sequence. 
easily  1  a*  follows: 


m^'ff 


(^^^^^^^^^ 


n 


Of  course,  it  is  not  necessary  in  any  sequence  that 
the  roots  of  the  chorda  must  always  be  at  the  base. 

The  following  example,  are  contrapuntal  sequences,  with 
seventh  and  ninth  added. 


:=tiUi^itT5Nfefe 


I     1 


E^S 


i;M 


wm. 


4 


ONV. 

uhord*,  rcjflaleil  a  third 

nio  liarmonio  sequenco* 


'^m^ 
^^^ 


^ •- 


^^ 


y  in  any  sequence  t^iat 
always  be  at  the  base. 

Urapuntal  sequences,  with 


« 


-J-4 


=F^ 


I    1 


» 


lI.AaKK's    IIAR.MONV. 


113 


-i=^^rE^ 


e^^m^^ 


^E^^^^m 


No.  1.  Sequence  of  suspended  seTentha ;  roots  fall  a,  fifth 
and  rise  a  fourth. 

No.  2.  Scijuenoe  of  suspended  sevenths ;  roots  rise  a  senond 
and  fall  a  third. 

No.  8..Sequenrc  of  suspended  ninths;  roots  rise  a  fourth 
and  fall  a  fifth. 

No.  4.  Sequence  of  suspended  ninths  ;  roots  fall  a  third  and 
rise  a  second 

No.  1  may  be  changed  into  tho  harmonic  sequence  (described 
on  page  68),  as  a  suooession  of  dominant  chords. 


il^i^^^^ 


TO 


If 


114  CLARKK'H   IIAHMO.NV. 

No.  2  may  b«  changed  into  »  harmonic  ••<|ueiioo  in  two  wayi. 


(^"^^^^I^ 


No.  1  is  »  Mquano*  of  dominant  obordi  raiolTing  on  tlie 
iiitii  (if  ibeir  toalo. 

No.  2  ii  a  iiequenMof  dominant  aliorda  with  roots  omitted, 
reMolving  on  their  tonio*. 


!  I 


u 


NV, 


iiequeiioo  in  twowayi. 


— — t 


m 


ordi  rtsoWing  on  the 
rdi  with  roots  omitted, 


CHAPTER  XIII. 

ModuIjATIon. — Moiliiliition  \n  tlio  net  of  pnnRing 
tVoin  one  koy  to  nnotlwr.  Tliero  in,  imfortuimHtly, 
no  wiiy  of  ilistinguiHliinjj  hetweon  niodiiliitionH  to 
related  nn»l  nioduIntiouH  to  non-rolntcd  kvya.  The 
term  tranHition  Ih  sonietimea  used  to  uignifv  a  sud- 
den change  to  a  remote  key.  It  would,  i)jrhat)H,  bo 
a  good  method  to  use  the  term  modulation  to  signify 
the  change  to  a  related  key,  and  transition  to  signify 
the  ciiange  to  a  non-related  key.  It  is  verj'  unfor- 
tunate, but  true,  nevertlielcss,  that  the  musical 
nomenclature  of  the  English  language  is  in  a  very 
confused  state. 

I  shall  use  the  word  modulation  in  its  generally 
accepted  sense — to  cover  all  possible  changes  of  key. 

All  modulations  may  be  reduced  to  four  rules  : 

Ist.  By  taking  advantage  of  the  fact  thnt  the 
dominant  chord  is  the  same,  whether  the  key  is 
major  or  minor. 

This  will  give  six  modulations  from  any  given 
key,  because  there  are  six  dominant  chords  in  every 
key. 

The  following  exiimples  contain  all  the  modulations  that  may 
be  made  by  this  rule,  from  the  key  of  C. 

(116) 


-  -  ■^.m^'^.^i^ 


li^T^ 


116 


CI-AB1\.E  S    HABMONY. 


*i#- 


i^^f^p 


In  1,  2  and  3  the  msyor  tonics  of  the  key  are  changed  to 
minor. 

No.  1  becomes  C  minor,  relative  minor  of  Eb. 

No.  2  becomes  O  minor,  relative  minor  of  Bt>. 

No.  3  becomes  F  minor,  relative  minor  of  Ab. 

In  4,  5  and  6  ttie  minor  tonics  of  the  scale  are  changed  to 
major. 

These  examples  are,  of  course,  mere  skeletonb,  being  too 
abrupt  to  have  any  musical  effect  as  they  stand ;  in  fact,  it 
might  almost  be  laid  down  as  a  rule  that  no  modulntion  has 
any  intrinsic  beauty;  it  depends  altogether  on  the  wny  it  is 
usi'd.  Some  of  the  most  beautiful  examples  in  the  works  of 
the  grent  masters  are  as  simple  as  possible ;  but  the  manner 
of  their  use  gives  them  all  their  exquisite  effect. 


ONY. 

a 


tP 


^'r--''"y"r- 


t  the  key  are  changed  to 

linor  of  Eb. 
linor  of  Bt>. 
inor  of  A\>. 
'  the  Boale  are  changed  to 


mere  skeletonb,  being  too 
ia  they  stand ;  in  fact,  it 
lie  that  no  modulntion  has 
[together  on  the  wny  it  is 
examples  in  tlio  works  of 
possible ;  but  the  manner 
[uisile  effect. 


Clarke's  harmony. 


117 


It  will  be  seen  that  by  extending  this  rulo  to  each 
new  key  that  is  reached,  that  it  is  possible  to  pass 
through  all  the  keys.  For  example,  the  first  modu- 
lation changes  the  key  to  E^ ;  then  by  applj'ing  the 
rule  to  tlie  chords  in  E^,  six  new  changes  would  be 
obtained. 

The  following  examples  will  show  how  effective  a  modula- 
tion of  this  kind  may  be  made. 


C  minor. 


^ 


i-ld- 


W^ 


^    J.      ^ 


-^- 


EE^ 


(i 


s^gi^i 


m=^ES^-=f-- 


*=«=«^ 


I     I 


±^i=^^^^^^iirl 


r==J:J^ 


fcx=t=t=^ 


■X '  '      '      ■      ' : — 


;■ 


'^ 


I'i 


III 


11 


Hi 


118 


CliARKB'a    HARMONY. 


C  major. 

I 


i 


W-- 


g?^=Ftf 


m^^^ 


?=i=p= 


i 


The  second  means  by  which  modulations  may  be 
made,  is  hy  taking  advantage  of  the  different  places 
in  which  a  major  or  a  minor  chord  may  be  found.     . 

A  major  chord  may  be  found  in  six  places,  viz. : 
As  a  tonic,  subdominant,  dominant,  sixth  of  a  minor 
scale  and  lowered  supertonic  of  a  major  or  minor 
scale. 


gJZ^gZ^Z^^ 


.a « 0-. 


1 


ONY. 


E3^ 


H 


modulations  may  be 
f  the  diiTerent  places 
)rd  may  be  found. 

I  in  six  places,  viz. : 
ant,  sixth  of  a  minor 
>f  a  major  or  minor 


_« ffl- 


1 


CI<A.BK£'8  HARMONY. 


119 


•^      I        '  or 


iT^ 


is=^. 


le^ 


(i?i 


^=P= 


i 


-^ 


No.  1.  C  major  as  a  subdominant.  (When  treating  a  chord 
as  a  Bubdominant  or  lowered  supertonic,  the  modulation  is 
more  decided  if  it  be  followed  by  the  second  inversion  of  the 
tonic.) 

No.  2.  C  major  as  a  dominant. 

No.  3.  C  major  as  chord  on  sixth  of  E  minor.  (This  modu- 
lation may  proceed  to  E  major,  in  accordance  with  the  rule 
that  any  chord  in  a  minor  key  may  be.  used  in  its  parallel 
major.) 

No.  4.  C  mnjor  as  lowered  supertonic  of  B  major  or  minor. 

The  following  harmonic  sequence  may  be  constructed  from 
this  last  example. 


ig=£^r,^=j§:=»-g" 


1 


■iHi^.'«»>*^i^B**ii^'@*a-SSirt*^SSl«i^»-^ 


m 


t 


i 


120 


CLARKE'S   llABMONY. 


Each  common  chord  bears  the  relation  of  tonio  to  the  ilomi- 
nant  that  precedes  it,  and  lowered  supertonic  to  the  dominant 
that  follows  it. 


The  following  examples  gite  the  modulations  that  may  be 
obtained  from  the  two  remaining  major  chords  in  the  key  of  C. 


^ 


m 


■j^tzf^zzz. 


5tZ«= 


i 


n 


F  us  dominant. 


F  an  isizth  of  A  minor. 


)  I  •'        I  'or 


m. 


z^— ^ 


^ 


-9- 


m 


F  IS  lowered  supertonic  of  K 


(}  ii><  ^ulidominant. 


O  iM  si-xtli  of  n  minor. 


NY. 

an  of  tonio  to  the  (Jonii- 
ertonio  to  iho  dominant 


>dulation8  that  may  he 
r  chords  in  the  key  of  C. 


J— H 


fcs 


^m 


X 


fcz«= 


^ 


m 


I  Blxtli  of  A  minor. 


m 


s^i 


X 


1 


a  iix  Hlxth  of  R  minor. 


CLAUKE  S   HARMONY 


191 


'■o-p- 


■■^~ 


X 


l§::^ 


1r 


^m^ 


a  as  loworod  xuportonic  of  F$. 


A  minor  chord  niaj'  be  found  in  six  pliicoH,  viz.  : 
Tonic  and  snlHlominant  in  a  minor  koy,  and  t^nper- 
tonic,  mediant  and  subniediant  in  a  major  key. 


l^^^lSif 


X 


ai; 


p^ll^E^la 


«t 


H 


A  minor  aa  subdomiuant  of  E. 


i=#i-^f=^4^i^ 


X 


jE^p^^ 


A  minor  aa  mediant  of  K  (third  degree). 


^i^l=3-^!^gl 


i 


A  minor  as  supcrtonic  of  G, 


m 


I 


122  clabke'b  uakmony. 

(It  would  be  superfluous  to  gire  any  more  exMnplea.     The 
pupil  ougbt  to  bo  able  to  construct  them  himself.) 

A  major  chord    may  have   an   augmented   sixth 
added  to  it. 


No.  1.  C  major,  changed  to  augmented  Rizth  on  sixth  degree 
of  E. 

No.  2.  C  major,  changed  to  augmented  sixth  on  lowered 
supertonio  of  B. 

No.  3,  G  major,  changed  to  augmented  sixth  on  sixth  of  B. 

No.  4.  Q  major,  changed  to  augmented  sikth  on  lowered 
supertonio  of  F#. 

A  major  and  minor  chord  may  bo  treated  as  the 
seventh,  ninth  and  eleventh  of  a  dominant  harmon3-, 
provided  the  fifth  from  the  root  is  added.     Thuf> 

C,  E,  O  may  be  the  seventh,  ninth  and  eleventh  from 

D,  by  adding  A,  the  fifth  from  the  root,  D. 


No.  1.  F,  changed  to  dominant  of  C. 
No.  2.  C,  changed  to  dominant  of  0. 


>NY. 

17  more  exhmples.    The 
m  liimself.) 

n   augmented   sixth 


ed  Bizth  on  sixth  degree 

>nted  Hizth  on  lowered 

ted  sixth  on  sixth  of  D. 
ented  eikth  on  lowered 

ly  bo  treated  as  the 
I.  dominant  liarmon3-, 
>ot  is  added.  Thus 
h  and  eleventh  from 
he  root,  D. 


clarke'8  iiakmony.  123 

No.  3.  E  minor,  changed  to  dominant  of  U. 
No.  4.  B  minor,  changed  to  dominant  of  F#. 

The  third  of  the  major  chord  may  bo  changed, 
thus : 


p=i 


i^^=ffi 


because  it  becomes  the  ninth  when  treated  as  above. 

Tiie  minor  chord  may  also  become  tiie  fifth, 
seventh  and  ninth  of  a  dominant  or  supertoniu  har- 
mony, b}'  adding  the  root  or  third  to  it. 


^^^^^m 


•«■  W     W  T5. 


^te^ 


X 


No.  1.  A  minor,  changed  to  dominant  of  0. 

No.  2.  D  minor,  changed  to  eupertonio  harmony  of  F. 

No.  8.  E  minor,  changed  to  dominant  of  D. 

The  third  means  of  modulation  is  by  the  chromatic 
alteration  of  chords.  Common  chords  may  be  chro- 
matically altered,  as  follows : 


(;  major. 


C  minor. 


to         or    i'i~  to         or     or"  ; 


i.  €.,  the  third  alone  or  the  third  and  fifth  of  a  major 
chord  may  be  lowered,  or  the  root  may  be  raised. 


124 


CLARKE'8   Il.VftMONT. 


The  tliird  alone  of  a  minor  chord  or  the  third  and 
fifth  may  be  raised,  or  the  fifth  may  be  lowered. 

In  the  above  example,  C,  E,  Q  is  major;  C,  E>,  0,  minor; 
r,  E\>,  0!»,  part  of  the  dominant  of  D>  or  D!»,  or  Biipertonio 
harmony  of  G>  or  Eb  ;  CJ^,  E,  O  is  pm  f  dominant  harmony 
of  D  or  B,  or  supertonio  harmony  ol'      ,ir  E. 


i 


1 


m 


No.  1.  C,  E!»,  0,  as  coming  from  Ab,  dominant  of  Db. 
No.  2.  C,  Eb,  O,  as  coming  from  F,  dominant  of  Bb. 
No.  3.  C,  Eb,  G,  as  coming  firom  F,  i.ipcrlonic  of  Eb. 
No.  4.  C,  Eb,  O,  as  coming  from  Db,  supertonio  of  G^. 

The  most  important  modnlationa  of  this  kind  are 
obtained  from  the  chromatic  alteration  of  groups  of 
four  notes  (see  page  64). 


1^ 


* 


m^mm 


l?t  group. 
Koot:  a. 


4tli. 
C. 


2.1i)r4lli. 
EiorC. 


3.1. 

r. 


Commencing  with  the  first  group,  the  third  may 
be  lowered  alone,  or  the  third  and  fifth  together,  or 
third,  fifth  and  seventh  together,  or  third  alone,  fol- 
lowed by  fif  h  and  seventh  together.     This  process 


iaiMHa* 


NT. 

d  or  the  third  and 
lay  bo  lowered. 

lojor;  C,  E>,  0,  minor; 

•>  or  H\>,  or  Btipertonio 

'{  dominant  harmony 

,.r  E. 


'-^&=S^- 


1 


4 


dominant  of  D!>. 
lominant  of  B':>. 
jporlonic  of  E!>. 
Bupertonic  of  0?. 

ons  of  this  kind  are 
oration  of  groups  of 


1.  3<I. 

r. 


roup,  tlie  third  maj' 
id  fifth  together,  or 
,  or  third  alone,  fol- 
ither.     This  process 


clabkk's  hak.monv.  125 

maybe  reversed  by  commencing  with  the  last  group 
in  the  above  example. 

In  the  following  examples  aro  gome  more  changes  of  this 
kind.     A  little  study  will  enable  the  pupil  to  oonstruol  others. 


The  last  means  of  modulating  is  by  the  enharmonic 
change  of  chords.  A  common  chord  may  be  changed 
as  foUoM's : 


g^g^^^ 


No.  1.  D!",  changed  to  CS,  dominant  of  F^. 
No.  2.  F#  minor,  changed  to  Qb  minor,  the  minor  subdomi- 
nant  of  Dt>. 


1S6 


Ct.ARKR  H    HARMONY. 


All  jincrmpntpd  sixth  chord  rany  bo  changed  to  a 
duinitmnt,  and  tho  rcvcrMc. 


^^P:^ 


.^m^- 


l^l^^l^^pi 


to  to 


Nob.  1  and  ;!.  Augmented  bixth,  changed  to  dominant  by 
enharraonio  alteration  of  the  sixth. 

Nos.  8  and  4.  Augmented  sixth,  changed  to  dominant  by 
cnhnrraonio  alteration  of  the  first,  third  and  fi(Mi. 

Nos.  5  ond  0.  Dominant,  changed  to  augmented  sixth  by 
enharmonic  alteration  of  tlie  seventh. 

Nos.  7  and  8.  Dominant,  changed  to  augmented  sixth  by 
enharmonic  oltcration  of  the  flrst,  third  and  fifth. 

The  most  pioliflc  source  of  enharmonic  modula- 
tion is  to  be  found  in  the  diminished  seventli  chord ;. 
This  chord,  it  will  be  remembered,  results  from 
adding  the  minor  ninth  to  a  dominant  or  superton!c 
harmony,  and  omitting  tho  root. 

Three  groups  of  sound}  form  all  tho  diminished 
snvonth  eliords.  Since  there  are  twelve  m.ijor  ehorla 
to  which  the  ninth  may  be  added,  it  follows  that 
each  group  must  bo  obtained  from  f  )ur  rootn  ;  al-.o, 


'  '  it^ijwwiwuliiii 


NV. 

ny  bo  changed  to  a 

8 

e 


to 
tnged  to  dominant  by 

inged  to  dominant  by 

[  and  fiftli. 

>  augmented  Hixth   by 

0  augmented  siztli  by 

1  and  fifth. 

nharmonic  inodiil".- 
led  seventli  chord ;. 
ercd,  results  fro-.u 
Inant  or  supcrtoivc 


all  the  diminished 
wclvo  major  ehor  la 
ed,  it  follows  that 
hi  fr)ur  rootn;  nl  o, 


t'l.ABKE'rt    KAKMUNY. 


127 


since  there  tiro  six  dominanta  In  every  scale,  it  fol- 
lows that  each  group  must  occur  Iwio;'  in  every 
8L-ale  as  a  dominant  harmony  ;  alio,  there  boing  six 
Hupcrtonio  chords  in  every  scale,  each  group  mur.t 
occur  twice  as  a  supertonic  harmony  in  every  scale. 
P'or  convcnicnca  we  will  number  the  groui):^  as  fol- 
lows :  Tiiat  from  dominant  of  C,  first;  from  domi- 
nant of  F,  second  ;  from  dominant  of  O,  third. 


Hooti:      a, 

Unmtnant  of      C, 

Suporton.  harm'y  of  l", 


E, 

A, 


(Db). 

(O.-). 
B,      AS 
(Ob). 


r,    D,    D,      A\ 

n;.,  o,  E,     iy,j. 


Roots:       I),       II,  Ats 

(o«). 

Domluantof       O,        E,  »>        B>. 

(c;) 

Suportonio  harmony  of  C,       A,  Oi;,       Ey 

(F|). 

No.  1  occurs  in  C,  as  dominant  of  C  and  dominant  of  its 
relatiye  minor. 

No.  2  occurs  in  C,  a')  dominant  of  F  and  dominant  of  its 
relative  minor. 

No.  3  occurs  in  C  ns  dominant  of  0  and  dominant  of  lis 
relative  minor. 

In  the  following  examples  are  all  tho  roaolution?  possib'o  to 
the  first  group.  Tho  pupil  can  easily  wi-ito  Ihouo  of  the  re- 
maining groups. 


IJX 


<'t,AKKK'"<    IIAKMilNV. 


f^fllYsrlT^-ffe^il 


Hoot:    (> 


RtNit:    r^i It, 

No  1.  Written  as  coming  fVotii  O  ;  renoWoil,  flrnt,  an  iloml- 
imnl  or  (';  Hooonil,  iim  Bupertuiiio  Iinrmnny  of  F. 

No.  'J.  Written  as  coining  from  E;  roKolvcil,  first,  uh  domi- 
nant of  A  ;  RocontI,  an  luperloiiio  harmony  of  I). 

No.  H.  Written  uh  voniinK  from  C# ;  renolveil,  flrsi,  nn  domi- 
nant of  F#  ;  Hccond,  iis  Nupcrtoniu  hnrmoiiy  of  U. 

No.  4.  Written  a8«oin!ng  from  !)• ;  ro^olvcd,  flml,  an  domi- 
nant of  K'j;  Hi'cond,  nt  Kiiportonic  linnnony  of  A  '. 

Olio  incinlM'r  of  a  <i;r(Mi|i  iiiav  ho  iuld  mikI  llio  ip 
inniiiiiiu;  three  mivv  be  niixod  a  seinitoiu'.  'I'ho  result 
is  a  (liimiiiaiit  or  siipertoiiic  chord  of  which  \\w  licld 
note  is  tlu!  root. 


11 


"^"-1; 


IS,  .—I 


^^Ei 


>\\. 


-jiar 


renoWod,  flMt,  an  ilomU 
rioiiy  of  K. 

rexolvpil,  first,  us  doml- 
noiiy  of  1>. 

renolveil,  flrHi,  i\«  domU 
■moiiy  of  U. 

ro.iolvcil,  flrHl,  nx  domU 
inony  of  A  >. 

1)0    lulfl    Mild    lllO  IP 

'initoiii'.  'I'ho  ri'Miilt 
111  of  whioli  tlio  lieltl 


•r:!?5f— r«- 


il 


clarkkV  iiakmunv. 


1S9 


No.  1.  V  held  ;  I  lie  chord  li.'oomei,  ftr»t,  dominant  of  Hl»,  or 
■econd,  utiperlonio  hi»riiioiiy  of  Ki'. 

No  '-'.  A 'held;  llu-  «liord  hocomeB,  flrtl,  dominftnl  of  Vf, 
or  necoiid,  miixTl  'iiio  hnrmoiiy  of  fl:*. 

;>',).  ;t.  B  hfld  ;  the  chord  hcooiiieM,  flml,  dominant  of  E,  or 
■econd,  iuporfonio  harmony  of  A. 

No  »  l>  hold  ;  Ihu  chord  hcoomen,  flfit,  dominant  of  0,  or 
ieoon<l,  dupertonio  harmony  of  ('. 

L-istly,  one  inomhcr  may  ).(•  Iicl<l,  tlio  remaining 
throe  niiHi'd  a  Hi'initniio,  iiml  tlic  nolo  tlmt  Ik-co??!*"* 
the  scventli,  may  l)e  clmnged  to  an  augmented  nixth. 


The  pupil  should  write  out  all  theiie  Changs'*  in  nil  the  groups 
repeatedly.  This  is  the  only  wny  to  become  familinr  with  them. 
It  would  take  too  much  space  to  write  examples  of  all  these 
various  modulations,  and  would,  besides,  be  of  very  little  real 
UHO  to  the  student.  The  bettor  way  is  to  try,  from  the  rules 
here  given,  to  construct  modulations.  A  littlo  perseverance 
will  accomplish  it.  Of  course,  it  is  possible  in  a  modulation 
to  mix  any  or  all  of  these  rules  together. 

The  works  of  Wagner,  Raff,  Chopin,  Qounod,  Schumann,  and 
others  among  the  modern  writers,  will  furnish  endless  examples 
of  ingenious  modulations  that  may  be  profitably  studied.  And 
there  is  no  posaible  modulation  that  the  rules  here  given  will 
not  explain. 


CHAPTER  XIV. 

Writing  in  Parts. — Music  is  said  to  be  written 
in  parts,  when  eacli  voice  (or  instrument)  has  an  in- 
dependent melody  of  its  own.  This  kind  of  writing 
belongs  properly  to  the  study  of  counterpoint ;  but 
the  object  of  this  chapter  is  to  give  some  idea  of  the 
process. 

1st.  In  tivo  parts. — The  following  intervals  may 
be  used  nt  anj'  time  :  Major  and  minor  third,  major 
and  minor  sixth,  augmented  fourth, diminished  fif:h, 
perfect  fifth  and  octave.  The  perfect  fifth  should 
be  avoided,  being  ineffective.  The  same  remark 
applies,  but  not  with  eqiuti  force,  to  the  octave  or 
unison.  The  octave  and  unison  make  the  best  end- 
ing. The  minor  second  ma}''  be  used  as  a  susp'^  nsion 
(it  results  from  the  inversion  of  a  suspended  seventh, 
see  page  107),  and  must  resolve  according  to  the  rules 
for  suspended  dissonants  (page  108). 


^ 


1 


Inversion  of 


i 


^ 


•^     r 


^ 


i 


(ISO) 


?;  i 


IV. 


mid  to  be  written 
•ument)  has  an  in- 
lis  kind  of  writing 
Liounterpoint ;  but 
e  some  idea  of  tlie 

ing  intervals  may 
ninor  tiiird,  major 
1,  diminished  fif:h, 
irfect  fifth  should 
'he  same  remark 
to  the  octave  or 
ake  the  be<5t  end- 
kI  as  asusjynsion 
ispended  seventh, 
irding  to  the  rules 

0. 


CLARKE'S    IIARMONV. 


131 


The  mnjor  second  maj-  be  used  .10  a  suspension, 
or  it  may  bo  used  na  part  of  a  dominant  chord  ;  but 
in  this  case  one  of  the  notes  nhould  (not  noeossnrily 
the  seventh,  as  in  the  preceding  case)  bu  held  from 
the  preceding  chord. 


Seventh  held. 


I 


i 


^m 


i 


B«ot  hold, 

The  augmented  second  may  be  used  as  follows ; 


It  represents  the  third  and  ninth  of  the  dominant 
harmonj' — the  ninth,  followed  by  th    root. 

The  dim.  lished  third  can  only  occur  as  a  passing 
note. 


i 


I     I 


The  augmented  fouri;h  may  be  used  at  any  time, 
but  it  '-ust  resolve — being  partof  a  dominant  chord, 
viz.,  third  and  seventh,  or  fifth  and  minor  ninth. 


m 


132 


CI.ARKK'8  iiabmo.vy. 


z^<^—-n 


Aujirmpiitoil  foiirtli  ns  third  nnd  seventh  in  dominant  of  C. 


i^^H 


AuKitinntcd  fourth  ii8  iiah  nnd  minor  ninth  li,  domlnnnt  of  A. 

The  diminished  fourtli  may  occur  as  a  retardation 
(it  is  always  the  retardation  of  the  fifth  of  a  chord). 


m 


The  root  of  the  second  chord  is  E.  The  remaining 
intervals  being  inversions  of  those  already  given, 
are,  of  ooiirse,  sulyect  to  the  same  rides. 

It  is  possible,  in  two  parts,  to  represent  the  har- 
mony very  effectively,  by  allowing  one  or  both  parts 
to  proceed  through  the  members  of  the  chord. 


^t^^jife^ 


r 

Bar  1  is  all  dominant  of  A. 

Bar  2.  First  beat,  (onio  of  A  ;  tho  rest  of  the  bar,  Uominant 
of  P.  It  is  important  to  remember  that  when  the  harmony 
ehangei,  the  dissonant  notes  must  resolve. 


ONY. 


ith  in  dominant  of  r. 


i 


ilnth  Ir,  dominant  of  A. 

3cur  as  a  retardation 
;he  fifth  of  a  chord). 


1  E.  The  remaining 
hose  already  given, 
ne  rides. 

o  represent  the  har- 
ig  one  or  both  parts 
of  the  chord. 


^ 


st  of  the  bar,  Uominant 
hat  when  (he  harmony 
e. 


MM 


ri.ARKE's   IIAIIMUNY. 


l;i:j 


The  angmenle<l  sixtii  cliord  may  bu  represented 
as  follows : 


i 


Or  as  follows : 


^m 


*     These  ar--^  the  only  ways  it  sounds  well  in  two 
parts. 

The  perfect  fourth  can  only  be  used  as  follows : 


^^m 


viz.,  as  retardation  of  third  of  a  chord. 
Or 


^^ 


^^ 


viz.,  one  or  both  parts  proceeding  through  tiie  meu. 
lu-r  (  of  the  chonl. 


---^  L^tf^'Vfeii-»>  i>r="«'^ 


11 


134  CLARKE'S  HARMONY. 

Or 

in  which  it  is  a  passing  note  on  the  chord  of  P. 

All  the  dissonantcs  and  the  perfect  fourth  may 
be  used  as  appoggiaturas  or  as  passing  notes. 

The  following  rules  must  be  observed  for  the  pro- 
gression of  the  parts : 

Ist.  Contrast  them  as  much  as  possible. 

2d.  Use   contrary  motion   in   preference   to   any 
other. 

3d.  Never  use  a  cross  or  false  relation. 

4th.  Never  proceed  by  parallel  motion  to  a  perfect 
fifth,  except  as  follows : 


i 


^ 


^=^=t: 


1 


(called  a  horn  passage).  Of  course,  this  does  not 
apply  in  a  passage  like  the  following,  in  which  the 
same  chord  is  repeated  in  another  position. 


1^ 


■*4ll|i»«| 


>NY. 


the  chord  of  F. 

perfect  fourth  may 
tassing  notes. 

•bserved  for  the  pro- 


s  possible, 
preference  to  any 

relation. 
1  motion  to  a  perfect 


ourse,  this  does  not 
Lowing,  in  which  the 
er  position. 


I 


clarke'8  harmony. 


185 


.5th.  Never  proceed  to  an  octave  in  parsilU'l  motion, 
unless  the  upper  part  rises  a  semitone. 

Gth.  Never  write  two  major  thirds  in  succession, 
whose  roots  are  less  than  a  perfect  fourth  apart. 


Bad. ""O*'- 


Last  of  all  and  most  important.  The  composition 
must  be  so  constructed  as  to  express  the  harmonic 
succession  as  definitely  as  if  it  were  in  four  parts. 

In  three  parts.— Ml  the  preceding  remarks  and 
rules  hold  good ;  but  the  following  are  relaxed,  viz., 
the  dominant  with  seventh,  or  any  of  the  dominant 
harmonies  can  be  struck  without  any  preparation ; 
also,  the  supertonic  harmonies.  The  following  table 
gives  the  best  way  of  representing  all  the  harmonies 
in  three  parts. 


i 


j»  -gt^  -g 


186 


olarkk's  harmony. 


Nc.  1.  Common  chord.     (Of  course,  all  may  he  inverted.) 
No.  2.  Dominant  or  supertonic  harmonies. 
No.  3.  Aunmented  sixth.  First,  when  followed  by  dominant; 
second,  when  followed  by  the  tonic. 


The  perfect  cadence  may  be  made  as  follows  in 
three  parts,  viz.,  the  tonic,  with  the  root  omitted  and 
tlie  fifth  doubled.  (It  is  only  the  position  tliat  en- 
ables us  to  recognize  this  as  the  chord  of  F.) 


i 


:f: 


J*.^. 


i 


Px    o 


w 


■»    -^ 


The  rules,  with  regard  to  proceeding  by  parallel 
motion  to  perfect  conconls,  are  relaxed,  with  rosranl 
to  the  lower  and  middle  or  middle  and  upper  parts ; 
but  are  still  binding  on  the  lower  and  ujiper  parts. 


Also,  two  major  thirds  may  ocr-ur  (see  above) 
between  the  lower  and  middle  or  middle  and  upper 
parts. 


MONY. 


3l 


le,  alt  may  he  inverted.) 

Tmonies. 

hen  followed  by  dominant ; 


)o  made  as  follows  in 
h  the  root  omitted  and 
y  the  position  that  en- 
he  chord  of  F.) 


proceeding  by  parallel 
re  relaxed,  with  roirard 
iddle  and  upper  parts ; 
iwer  and  ujiper  parts. 


lay  ocpiir   (see   above) 
le  or  middle  and  upper 


CLABKE's    IIARMOW. 


^^^m 


ite. 


W=f^^zL^^ 


3^ 


f^ 


137 


No.  1.  Fifth  in  parallel  motion  between  lower  and  middle 
parts. 

Mo.  2.  Fifth  in  parallel  motion  between  middle  and  upper 
parts. 

No.  3.  Major  third  between  lower  and  middle  parts. 

No.  4.  Major  third  between  middle  and  upper  parts. 

No.  3  is  much  better  than  No.  4. 


With  regard  to  fonr-part  writing,  nothing  new 
need  be  said.  It  is  subject  to  the  same  rules  a.s 
three-part,  and  differs  only  in  its  greater  variety  and 
copiousness. 


138 


Clarke's  iiARMONr. 


The  following  examples  are  intended  principally 
to  show  the  manner  of  using  passing  notes  and 
'ipPoggittt'Tas.  One  of  the  best  ways  to  study  free 
composition  in  two  parts,  is  by  examining  the  violin 
(Inots  of  Spohr,  Pleyel  or  Viotti.  For  three-part 
writing,  the  string  trios  of  Beethoven  and  Mozart. 

Of  course,  in  all  these  compositions  there  are  fre- 
quently four  and  even  more  parts  produced  by  play- 
in^^  double  notes.  Also,  many  parts  are  merely 
f  1;>3  and  accompaniments.  Still  there  are  plenty 
cf  I'xamples  of  pure  two  and  three-part  writings  to 
be  found  in  them.  Perhaps  the  finest  specimen  of 
t-.vo-part  writing  in  the  world,  is  the  concerto  for 
two  violins,  by  Bach. 


IM 


lONir. 

intended  principnlly 
J  passing  notes  and 
3t  waj-s  to  study  free 

examining  the  violin 
otti.  For  tlirce-part 
tiioven  and  Mozart. 

ositions  tliere  are  fre- 
rts  produced  by  play- 
ly  parts  are  merely 
Still  there  are  plenty 
;hree-part  writings  to 
le  finest  specimen  of 
is  the  concerto  for 


CLARKE'S   IIABMONY. 


1S» 


Tlio  threi-  following  examples  are  founded  on  this 
harmony. 


5^-E^ 


.rSS^JSS^ 


TO^jT^ 


T^ 


i 


In  two  parts : 


^^^ 


MONA*. 


?^-i^Lib 


9 


^m 


T 


TT 


^^^^ 


f 


=^-#' 


:.-.r=f=3C 


^^^ 


^^^ 


S=i: 


8 r-T- 


(*-- 


CI.ARKKS    IIAIIMONY. 


141 


,i^^_^^[^P 


zqir. 


,p?:=^^ 


JTi=£. 


;:^- 


^ 


mi 


■tr 


.^ 


i^m 


^5=25= 


®- 


iT=P;:^',J^ 


^^P^P 


■^    ■•■ 


IH^  M         #         ^ 


|,g?pE='=»3g4-^^ 


^^slp. 


CLARKK'H    IIAllMONV. 


i_J_,4_itiJj-^,-^ 


'^^fE^'^ 


=.:ip|tf=to:sl: 


r 


i 


■^^' 


I     *.        i       J         !     x^i.*J 


lONV. 


-J. 


Uii: 


1^^ 


L_J^_ , 


CLAKKEli  IIARMUNY. 


148 


J  i  . 


^ — #■ 


( 


1^^^^ 


S 


i-4i 


;  _b^ ,  iA..^_^i 


s 


a 


§1^?^ 


\^^L_y — 


m^. 


i 


CONCLUSION. 

The  8tudei.t,  who  has  thoroughly  mastered  tliis 
course,  should  be  i)repared  for  the  study  of  couuter- 
point,  fugue,  canon,  and  the  various  forms  of  com- 
position. It  is  difficult  to  study  harmony  without  a 
teacher,  and  almost  impossible  to  study  these  higher 
branches  without  a  guide  at  first. 

I  have  omitted  any  explanation  of  the  figuring  of 
chords  (thorough  bass).  Tliere  are  hundreds  of 
works  Avherein  all  tlie  information  wished  for  may 
be  obtained  on  tliis  subject. 

For  tlie  study  of  strict  counterpoint.  Cherubim's 
is  perhaps  the  best  work.  For  the  study  of  form, 
no  work  will  suffice.  Some  good  ideas  on  this  -ib- 
ject  may  be  obtained  from  the  works  of  Dr.  Marx. 
Finally,  constant  writing  is  the  only  way  to  learn  to 
write  well.  No  amount  of  genius  will  make  up  for 
the  lack  of  hard.work. 


(U4) 


^-^iOnwi, 


M 


:oN. 

ughl}'  mastered  tliis 
the  study  of  coiiuter- 
rious  forms  of  com- 
y  harmony  without  a 
to  study  these  higher 

3t. 

iion  of  the  figuring  of 
ere  are  hundreds  of 
ition  wished  for  may 


nterpoint,  Cherubini's 
or  the  study  of  form, 
ood  ideas  on  this  "'ib- 
e  works  of  Dr.  Marx, 
e  only  waj'  to  learn  to 
luius  will  make  up  for 


